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The simplest single-field inflation models capture all the relevant contributions to the patterns in the Cosmic Microwave Background (CMB) observed today. A key assumption in these models is that the quantum inflationary fluctuations that source such patterns are generated by a particular quantum state -- the Bunch-Davies (BD) state. While this is a well-motivated choice from a theoretical perspective, the question arises of whether current data can rule out other, also well motivated, choices of states. In particular, as we previously demonstrated in arXiv:2104.13410 [hep-th], entanglement is naturally and inevitably dynamically generated during inflation given the presence of a "rolling" spectator scalar field -- and the resulting entangled state will yield a primordial power spectrum with potentially measurable deviations compared to the canonical BD result. For this work we developed a perturbative framework to allow a systematic exploration of constraints on (or detection of) entangled states with Planck CMB data using Monte Carlo techniques. We have found that most entangled states accessible with our framework are consistent with the data. One would have to expand the framework to allow a greater variety of entangled states in order to saturate the Planck constraints and more systematically explore any preferences the data may have among the different possibilities., Comment: 37 pages, 12 figures, 3 appendices. V2: Final version accepted for publication in JCAP. Changes: References added and minor clarifications to the presentation. Our results and conclusions are unchanged

La formación en ciencia, tecnología, ingeniería y matemáticas se considera clave para resolver muchos de los desafíos actuales y futuros de la humanidad, por lo cual la tendencia mundial en educación es fomentar el pensamiento computacional y la programación, especialmente en los niveles educativos preuniversitarios. A pesar de la atención general en ciencias de la computación, muchos docentes no tienen las habilidades profesionales en informática o pensamiento computacional, o no tienen presente nuevos enfoques de la didáctica de la programación. En este trabajo se describe una experiencia de formación en didáctica de la programación destinada a docentes de la región, realizada desde el 2015 al 2017. Para evaluar el impacto que esta capacitación tuvo en el contexto de desempeño de los docentes y en su propia formación, se realizó una encuesta a los participantes de este proceso formativo. Los resultados permiten inferir que los docentes están altamente motivados para incorporar la programación en sus espacios curriculares, que adhieren al enfoque didáctico propuesto y que son conscientes de los beneficios de promover el pensamiento computacional en las escuelas y, en la mayoría de los casos, los docentes han cambiado su percepción sobre la enseñanza de la programación., Instruction in science, technology, engineering and mathematics is considered key to solve many of the current and future challenges for humanity. Therefore, the worldwide trend in education is to promote the discipline of programming and computational thinking, especially in pre-universitary educational environments. In spite of the general attention computer science has gotten lately, many teachers do not have the professional skills pertaining to programming and computer science, or they are not aware of the new approaches of programming didactics. In this article we describe a training course in programming didactics directed to teachers at local schools, which has taken place from 2015 to 2017. In order to assess the effect this training has had on the teachers' performance and their own knowledge, a survey was conducted among participants of this educational process. The results from the aforementioned survey show that the teachers are highly motivated to incorporate programming in their syllabuses. It also shows that they adhere to the proposed teaching approach and that they are aware of the benefits that come from promoting computational thinking in schools and that, in most cases, they have changed their perception of programming didactics.

La formación en ciencia, tecnología, ingeniería y matemáticas se considera clave para resolver muchos de los desafíos actuales y futuros de la humanidad, por lo cual la tendencia mundial en educación es fomentar el pensamiento computacional y la programación, especialmente en los niveles educativos preuniversitarios. A pesar de la atención general en ciencias de la computación, muchos docentes no tienen las habilidades profesionales en informática o pensamiento computacional, o no tienen presente nuevos enfoques de la didáctica de la programación. En este trabajo se describe una experiencia de formación en didáctica de la programación destinada a docentes de la región, realizada desde el 2015 al 2017. Para evaluar el impacto que esta capacitación tuvo en el contexto de desempeño de los docentes y en su propia formación, se realizó una encuesta a los participantes de este proceso formativo. Los resultados permiten inferir que los docentes están altamente motivados para incorporar la programación en sus espacios curriculares, que adhieren al enfoque didáctico propuesto y que son conscientes de los beneficios de promover el pensamiento computacional en las escuelas y, en la mayoría de los casos, los docentes han cambiado su percepción sobre la enseñanza de la programación., Instruction in science, technology, engineering and mathematics is considered key to solve many of the current and future challenges for humanity. Therefore, the worldwide trend in education is to promote the discipline of programming and computational thinking, especially in pre-universitary educational environments. In spite of the general attention computer science has gotten lately, many teachers do not have the professional skills pertaining to programming and computer science, or they are not aware of the new approaches of programming didactics. In this article we describe a training course in programming didactics directed to teachers at local schools, which has taken place from 2015 to 2017. In order to assess the effect this training has had on the teachers' performance and their own knowledge, a survey was conducted among participants of this educational process. The results from the aforementioned survey show that the teachers are highly motivated to incorporate programming in their syllabuses. It also shows that they adhere to the proposed teaching approach and that they are aware of the benefits that come from promoting computational thinking in schools and that, in most cases, they have changed their perception of programming didactics.

We propose a new technique to study fast transitions during inflation, by studying the dynamics of quantum quenches in an $O(N)$ scalar field theory in de Sitter spacetime. We compute the time evolution of the system using a non-perturbative large-$N$ limit approach. We derive the self-consistent mass equation for several physically relevant transitions of the parameters of the theory, in a slow motion approximation. Our computations reveal that the effective mass after the quench evolves in the direction of recovering its value before the quench, but stopping at a different asymptotic value, in which the mass squared is strictly positive. Furthermore, we tentatively find situations in which the effective mass squared can be temporarily negative, thus breaking the $O(N)$ symmetry of the system for a certain time, only to then come back to a positive value, restoring the symmetry. We argue the relevance of our new method in a cosmological scenario., Comment: 30 pages, 10 figures. v2: minor changes and details added. Matches version published in PRD

Attempts to modify gravity in the infrared typically require a screening mechanism to ensure consistency with local tests of gravity. These screening mechanisms fit into three broad classes; we investigate theories which are capable of exhibiting more than one type of screening. Specifically, we focus on a simple model which exhibits both Vainshtein and kinetic screening. We point out that due to the two characteristic length scales in the problem, the type of screening that dominates depends on the mass of the sourcing object, allowing for different phenomenology at different scales. We consider embedding this double screening phenomenology in a broader cosmological scenario and show that the simplest examples that exhibit double screening are radiatively stable., Comment: 36 pages, 5 figures

Attempts to modify gravity in the infrared typically require a screening mechanism to ensure consistency with local tests of gravity. These screening mechanisms fit into three broad classes; we investigate theories which are capable of exhibiting more than one type of screening. Specifically, we focus on a simple model which exhibits both Vainshtein and kinetic screening. We point out that due to the two characteristic length scales in the problem, the type of screening that dominates depends on the mass of the sourcing object, allowing for different phenomenology at different scales. We consider embedding this double screening phenomenology in a broader cosmological scenario and show that the simplest examples that exhibit double screening are radiatively stable., Comment: 36 pages, 5 figures

We propose a new technique to study fast transitions during inflation, by studying the dynamics of quantum quenches in an $O(N)$ scalar field theory in de Sitter spacetime. We compute the time evolution of the system using a non-perturbative large-$N$ limit approach. We derive the self-consistent mass equation for several physically relevant transitions of the parameters of the theory, in a slow motion approximation. Our computations reveal that the effective mass after the quench evolves in the direction of recovering its value before the quench, but stopping at a different asymptotic value, in which the mass squared is strictly positive. Furthermore, we tentatively find situations in which the effective mass squared can be temporarily negative, thus breaking the $O(N)$ symmetry of the system for a certain time, only to then come back to a positive value, restoring the symmetry. We argue the relevance of our new method in a cosmological scenario., Comment: 30 pages, 10 figures. v2: minor changes and details added. Matches version published in PRD

Attempts to modify gravity in the infrared typically require a screening mechanism to ensure consistency with local tests of gravity. These screening mechanisms fit into three broad classes; we investigate theories which are capable of exhibiting more than one type of screening. Specifically, we focus on a simple model which exhibits both Vainshtein and kinetic screening. We point out that due to the two characteristic length scales in the problem, the type of screening that dominates depends on the mass of the sourcing object, allowing for different phenomenology at different scales. We consider embedding this double screening phenomenology in a broader cosmological scenario and show that the simplest examples that exhibit double screening are radiatively stable., Comment: 36 pages, 5 figures

In de Rham-Gabadadze-Tolley (dRGT) massive gravity and bigravity, a non-minimal matter coupling involving both metrics generically re-introduces the Boulware--Deser (BD) ghost. A non-minimal matter coupling via a simple, yet specific composite metric has been proposed, which eliminates the BD ghost below the strong coupling scale. Working explicitly in the metric formulation and for arbitrary spacetime dimensions, we show that this composite metric is the unique consistent non-minimal matter coupling below the strong coupling scale, which emerges out of two diagnostics, namely, absence of Ostrogradski ghosts in the decoupling limit and absence of the BD ghost from matter quantum loop corrections., Comment: v2: references added, matches accepted version in Physics Letters B v1: 6 pages, two-column

In de Rham-Gabadadze-Tolley (dRGT) massive gravity and bigravity, a non-minimal matter coupling involving both metrics generically re-introduces the Boulware--Deser (BD) ghost. A non-minimal matter coupling via a simple, yet specific composite metric has been proposed, which eliminates the BD ghost below the strong coupling scale. Working explicitly in the metric formulation and for arbitrary spacetime dimensions, we show that this composite metric is the unique consistent non-minimal matter coupling below the strong coupling scale, which emerges out of two diagnostics, namely, absence of Ostrogradski ghosts in the decoupling limit and absence of the BD ghost from matter quantum loop corrections., Comment: v2: references added, matches accepted version in Physics Letters B v1: 6 pages, two-column

If the amplitude of primordial gravitational waves is measured in the near-future, what could it tell us about bigravity? To address this question, we study massive bigravity theories by focusing on a region in parameter space which is safe from known instabilities. Similarly to investigations on late time constraints, we implicitly assume there is a successful implementation of the Vainshtein mechanism which guarantees that standard cosmological evolution is largely unaffected. We find that viable bigravity models are subject to far less stringent constraints than massive gravity, where there is only one set of (massive) tensor modes. In principle sensitive to the effective graviton mass at the time of recombination, we find that in our setup the primordial tensor spectrum is more responsive to the dynamics of the massless tensor sector rather than its massive counterpart. We further show there are intriguing windows in the parameter space of the theory which could potentially induce distinctive signatures in the B-modes spectrum., Comment: 20 pages, 1 table, 1 figure

In de Rham-Gabadadze-Tolley (dRGT) massive gravity and bigravity, a non-minimal matter coupling involving both metrics generically re-introduces the Boulware--Deser (BD) ghost. A non-minimal matter coupling via a simple, yet specific composite metric has been proposed, which eliminates the BD ghost below the strong coupling scale. Working explicitly in the metric formulation and for arbitrary spacetime dimensions, we show that this composite metric is the unique consistent non-minimal matter coupling below the strong coupling scale, which emerges out of two diagnostics, namely, absence of Ostrogradski ghosts in the decoupling limit and absence of the BD ghost from matter quantum loop corrections., Comment: v2: references added, matches accepted version in Physics Letters B v1: 6 pages, two-column

If the amplitude of primordial gravitational waves is measured in the near-future, what could it tell us about bigravity? To address this question, we study massive bigravity theories by focusing on a region in parameter space which is safe from known instabilities. Similarly to investigations on late time constraints, we implicitly assume there is a successful implementation of the Vainshtein mechanism which guarantees that standard cosmological evolution is largely unaffected. We find that viable bigravity models are subject to far less stringent constraints than massive gravity, where there is only one set of (massive) tensor modes. In principle sensitive to the effective graviton mass at the time of recombination, we find that in our setup the primordial tensor spectrum is more responsive to the dynamics of the massless tensor sector rather than its massive counterpart. We further show there are intriguing windows in the parameter space of the theory which could potentially induce distinctive signatures in the B-modes spectrum., Comment: 20 pages, 1 table, 1 figure

Recently, several works have investigated the coupling to matter in ghost-free massive (bi-&multi-)gravity and a new effective coupling to matter has been proposed. In this note we clarify some confusion on the existence and the implications of a ghost above the strong coupling scale. We confirm that the standard constraint which is otherwise typically present in this type of theories disappears on generic backgrounds as soon as this new coupling is considered. This implies the re-emergence of the Boulware-Deser ghost. Nevertheless the absence of ghost in the decoupling limit implies that the cut-off scale (if identified with the scale at which the ghost enters) is higher than the strong coupling scale. Therefore there is a valid interesting region of applicability for these couplings at scales below the cut-off., Comment: 8 pages. v2: minor typos fixed & extended discussion on ghosts above cut-off

Recently, several works have investigated the coupling to matter in ghost-free massive bigravity and multigravity and a new effective coupling to matter has been proposed. In this paper we clarify some confusion on the existence and the implications of a ghost above the strong coupling scale. We confirm that the standard constraint which is otherwise typically present in this type of theories disappears on generic backgrounds as soon as this new coupling is considered. This implies the reemergence of the BoulwareDeser ghost. Nevertheless the absence of ghost in the decoupling limit implies that the cutoff scale (if identified with the scale at which the ghost enters) is higher than the strong coupling scale. Therefore there is a valid interesting region of applicability for these couplings at scales below the cutoff., QC 20150225

Recently, several works have investigated the coupling to matter in ghost-free massive bigravity and multigravity and a new effective coupling to matter has been proposed. In this paper we clarify some confusion on the existence and the implications of a ghost above the strong coupling scale. We confirm that the standard constraint which is otherwise typically present in this type of theories disappears on generic backgrounds as soon as this new coupling is considered. This implies the reemergence of the BoulwareDeser ghost. Nevertheless the absence of ghost in the decoupling limit implies that the cutoff scale (if identified with the scale at which the ghost enters) is higher than the strong coupling scale. Therefore there is a valid interesting region of applicability for these couplings at scales below the cutoff.

We investigate the coupling to matter in ghost-free massive (bi-)gravity. When species in the matter sector couple covariantly to only one metric, we show that at one--loop these couplings do not spoil the special structure of the graviton potential. When the same species couples directly to both metrics we show that a ghost is present at the classical level and that loops destroy the special structure of the potential at an unacceptably low scale. We then propose a new `composite' effective metric built out of both metrics. When matter fields couple covariantly to this effective metric, the would be Boulware--Deser ghost is absent in different representative limits. At one--loop such couplings do not detune the special structure of the potential. We conjecture that matter can couple covariantly to that effective metric in all generality without introducing any Boulware--Deser ghost below a cut-off scale parametrically larger than the strong coupling scale. We also discuss alternative couplings to matter where the kinetic and potential terms of the matter field couple to different metrics. In both cases we discuss preliminary implications for cosmology., Comment: v3: discussions on ghost and FLRW solutions clarified, all results unchanged

We investigate the coupling to matter in ghost-free massive (bi-)gravity. When species in the matter sector couple covariantly to only one metric, we show that at one--loop these couplings do not spoil the special structure of the graviton potential. When the same species couples directly to both metrics we show that a ghost is present at the classical level and that loops destroy the special structure of the potential at an unacceptably low scale. We then propose a new `composite' effective metric built out of both metrics. When matter fields couple covariantly to this effective metric, the would be Boulware--Deser ghost is absent in different representative limits. At one--loop such couplings do not detune the special structure of the potential. We conjecture that matter can couple covariantly to that effective metric in all generality without introducing any Boulware--Deser ghost below a cut-off scale parametrically larger than the strong coupling scale. We also discuss alternative couplings to matter where the kinetic and potential terms of the matter field couple to different metrics. In both cases we discuss preliminary implications for cosmology., Comment: v3: discussions on ghost and FLRW solutions clarified, all results unchanged

Recently, several works have investigated the coupling to matter in ghost-free massive (bi-&multi-)gravity and a new effective coupling to matter has been proposed. In this note we clarify some confusion on the existence and the implications of a ghost above the strong coupling scale. We confirm that the standard constraint which is otherwise typically present in this type of theories disappears on generic backgrounds as soon as this new coupling is considered. This implies the re-emergence of the Boulware-Deser ghost. Nevertheless the absence of ghost in the decoupling limit implies that the cut-off scale (if identified with the scale at which the ghost enters) is higher than the strong coupling scale. Therefore there is a valid interesting region of applicability for these couplings at scales below the cut-off., Comment: 8 pages. v2: minor typos fixed & extended discussion on ghosts above cut-off

The latest results from PLANCK impose strong constraints on features in the spectrum of the curvature perturbations from inflation. We analyse the possibility of particle production induced by sharp turns of the trajectory in field space in inflation models with multiple fields. Although the evolution of the background fields can be altered by particle production, we find rather modest changes in the power spectrum even for the most extreme case in which the entire kinetic energy of the scalar fields is converted into particles., Comment: 33 pages, 6 figures, matches published version

We investigate the coupling to matter in ghost-free massive (bi-)gravity. When species in the matter sector couple covariantly to only one metric, we show that at one--loop these couplings do not spoil the special structure of the graviton potential. When the same species couples directly to both metrics we show that a ghost is present at the classical level and that loops destroy the special structure of the potential at an unacceptably low scale. We then propose a new `composite' effective metric built out of both metrics. When matter fields couple covariantly to this effective metric, the would be Boulware--Deser ghost is absent in different representative limits. At one--loop such couplings do not detune the special structure of the potential. We conjecture that matter can couple covariantly to that effective metric in all generality without introducing any Boulware--Deser ghost below a cut-off scale parametrically larger than the strong coupling scale. We also discuss alternative couplings to matter where the kinetic and potential terms of the matter field couple to different metrics. In both cases we discuss preliminary implications for cosmology., Comment: v3: discussions on ghost and FLRW solutions clarified, all results unchanged

We investigate the stability of a class of derivative theories known as $P(X)$ and Galileons against corrections generated by quantum effects. We use an exact renormalisation group approach to argue that these theories are stable under quantum corrections at all loops in regions where the kinetic term is large compared to the strong coupling scale. This is the regime of interest for screening or Vainshtein mechanisms, and in inflationary models that rely on large kinetic terms. Next, we clarify the role played by the symmetries. While symmetries protect the form of the quantum corrections, theories equipped with more symmetries do not necessarily have a broader range of scales for which they are valid. We show this by deriving explicitly the regime of validity of the classical solutions for $P(X)$ theories including Dirac-Born-Infeld (DBI) models, both in generic and for specific background field configurations. Indeed, we find that despite the existence of an additional symmetry, the DBI effective field theory has a regime of validity similar to an arbitrary $P(X)$ theory. We explore the implications of our results for both early and late universe contexts. Conversely, when applied to static and spherical screening mechanisms, we deduce that the regime of validity of typical power-law $P(X)$ theories is much larger than that of DBI., Comment: v1: 48 pages, 2 figures, 1 table; v2: references added and typos fixed, results unchanged. v3: matches version published in JCAP, 54 pages

We investigate the coupling to matter in ghost-free massive (bi-)gravity. When species in the matter sector couple covariantly to only one metric, we show that at one--loop these couplings do not spoil the special structure of the graviton potential. When the same species couples directly to both metrics we show that a ghost is present at the classical level and that loops destroy the special structure of the potential at an unacceptably low scale. We then propose a new `composite' effective metric built out of both metrics. When matter fields couple covariantly to this effective metric, the would be Boulware--Deser ghost is absent in different representative limits. At one--loop such couplings do not detune the special structure of the potential. We conjecture that matter can couple covariantly to that effective metric in all generality without introducing any Boulware--Deser ghost below a cut-off scale parametrically larger than the strong coupling scale. We also discuss alternative couplings to matter where the kinetic and potential terms of the matter field couple to different metrics. In both cases we discuss preliminary implications for cosmology., Comment: v3: discussions on ghost and FLRW solutions clarified, all results unchanged

We investigate the stability of a class of derivative theories known as $P(X)$ and Galileons against corrections generated by quantum effects. We use an exact renormalisation group approach to argue that these theories are stable under quantum corrections at all loops in regions where the kinetic term is large compared to the strong coupling scale. This is the regime of interest for screening or Vainshtein mechanisms, and in inflationary models that rely on large kinetic terms. Next, we clarify the role played by the symmetries. While symmetries protect the form of the quantum corrections, theories equipped with more symmetries do not necessarily have a broader range of scales for which they are valid. We show this by deriving explicitly the regime of validity of the classical solutions for $P(X)$ theories including Dirac-Born-Infeld (DBI) models, both in generic and for specific background field configurations. Indeed, we find that despite the existence of an additional symmetry, the DBI effective field theory has a regime of validity similar to an arbitrary $P(X)$ theory. We explore the implications of our results for both early and late universe contexts. Conversely, when applied to static and spherical screening mechanisms, we deduce that the regime of validity of typical power-law $P(X)$ theories is much larger than that of DBI., Comment: v1: 48 pages, 2 figures, 1 table; v2: references added and typos fixed, results unchanged. v3: matches version published in JCAP, 54 pages

Recently, several works have investigated the coupling to matter in ghost-free massive (bi-&multi-)gravity and a new effective coupling to matter has been proposed. In this note we clarify some confusion on the existence and the implications of a ghost above the strong coupling scale. We confirm that the standard constraint which is otherwise typically present in this type of theories disappears on generic backgrounds as soon as this new coupling is considered. This implies the re-emergence of the Boulware-Deser ghost. Nevertheless the absence of ghost in the decoupling limit implies that the cut-off scale (if identified with the scale at which the ghost enters) is higher than the strong coupling scale. Therefore there is a valid interesting region of applicability for these couplings at scales below the cut-off., Comment: 8 pages. v2: minor typos fixed & extended discussion on ghosts above cut-off

We investigate the coupling to matter in ghost-free massive (bi-)gravity. When species in the matter sector couple covariantly to only one metric, we show that at one--loop these couplings do not spoil the special structure of the graviton potential. When the same species couples directly to both metrics we show that a ghost is present at the classical level and that loops destroy the special structure of the potential at an unacceptably low scale. We then propose a new `composite' effective metric built out of both metrics. When matter fields couple covariantly to this effective metric, the would be Boulware--Deser ghost is absent in different representative limits. At one--loop such couplings do not detune the special structure of the potential. We conjecture that matter can couple covariantly to that effective metric in all generality without introducing any Boulware--Deser ghost below a cut-off scale parametrically larger than the strong coupling scale. We also discuss alternative couplings to matter where the kinetic and potential terms of the matter field couple to different metrics. In both cases we discuss preliminary implications for cosmology., Comment: v3: discussions on ghost and FLRW solutions clarified, all results unchanged

We investigate the stability of a class of derivative theories known as $P(X)$ and Galileons against corrections generated by quantum effects. We use an exact renormalisation group approach to argue that these theories are stable under quantum corrections at all loops in regions where the kinetic term is large compared to the strong coupling scale. This is the regime of interest for screening or Vainshtein mechanisms, and in inflationary models that rely on large kinetic terms. Next, we clarify the role played by the symmetries. While symmetries protect the form of the quantum corrections, theories equipped with more symmetries do not necessarily have a broader range of scales for which they are valid. We show this by deriving explicitly the regime of validity of the classical solutions for $P(X)$ theories including Dirac-Born-Infeld (DBI) models, both in generic and for specific background field configurations. Indeed, we find that despite the existence of an additional symmetry, the DBI effective field theory has a regime of validity similar to an arbitrary $P(X)$ theory. We explore the implications of our results for both early and late universe contexts. Conversely, when applied to static and spherical screening mechanisms, we deduce that the regime of validity of typical power-law $P(X)$ theories is much larger than that of DBI., Comment: v1: 48 pages, 2 figures, 1 table; v2: references added and typos fixed, results unchanged. v3: matches version published in JCAP, 54 pages

The latest results from PLANCK impose strong constraints on features in the spectrum of the curvature perturbations from inflation. We analyse the possibility of particle production induced by sharp turns of the trajectory in field space in inflation models with multiple fields. Although the evolution of the background fields can be altered by particle production, we find rather modest changes in the power spectrum even for the most extreme case in which the entire kinetic energy of the scalar fields is converted into particles., Comment: 33 pages, 6 figures, matches published version

The effective field theory (EFT) of inflation has become the preferred method for computing cosmological correlation functions of the curvature fluctuation, $\zeta$. It makes explicit use of the soft breaking of time diffeomorphisms by the inflationary background to organize the operators expansion in the action of the Goldstone mode $\pi$ associated with this breaking. Despite its ascendancy, there is another method for calculating $\zeta$ correlators, involving the direct calculation of the so-called Horndeski action order by order in powers of $\zeta$ and its derivatives. The question we address in this work is whether or not the $\zeta$ correlators calculated in these seemingly different ways are in fact the same. The answer is that the actions to cubic order in either set of variables do indeed give rise to the same $\zeta$ bispectra, but that to make this equivalence manifest requires a careful understanding of the non-linear transformations relating $\pi$ to $\zeta$ and how boundary terms in the actions are affected by imposing this relation. As a by product of our study we find that the calculations in the $\pi$ language can be simplified considerably in a way that allows us to use only the linear part of the $\pi-\zeta$ relation simply by changing the coefficients of some of the operators in the EFT. We also note that a proper accounting of the boundary terms will be of the greatest importance when computing the bispectrum for more general initial states than the Bunch-Davies one., Comment: v1: 20 pages, 1 figure. v2: references and minor clarifications added, results remain unchanged; matches version to be published in JCAP

We compute the one-loop quantum corrections to the potential of ghost-free massive gravity. We show how the mass of external matter fields contribute to the running of the cosmological constant, but do not change the ghost-free structure of the massive gravity potential at one-loop. When considering gravitons running in the loops, we show how the structure of the potential gets destabilized at the quantum level, but in a way which would never involve a ghost with a mass smaller than the Planck scale. This is done by explicitly computing the one-loop effective action and supplementing it with the Vainshtein mechanism. We conclude that to one-loop order the special mass structure of ghost-free massive gravity is technically natural., Comment: v2: References added, 29 pages, 7 figures

We present the first 3+1-dimensional numerical simulations of scalar fields with non-minimal kinetic terms. As an example, we examine the existence and stability of preheating in the presence of a Dirac-Born-Infeld (DBI) inflaton coupled to a canonical matter field. The simulations represent the full non-linear theory in the presence of an expanding Universe. We show that parametric resonance in the matter field, along with self-resonance in the inflaton, repopulate the Universe with matter particles as efficiently as in traditional preheating., Comment: 5 pages, 3 figures; note correction to parameter value in first paragraph of Numerical Simulations section (typographical error in published version)

We provide a formula for the scaling behaviour of the inflationary bispectrum in the 'squeezed' limit where one momentum becomes much smaller than the other two. This determines the scaling of the halo bias at low wavenumber and will be an important observable for the next generation of galaxy surveys. Our formula allows it to be predicted for the first time for a generic inflationary model with multiple light, canonically-normalized scalar fields., Comment: 5 pages, 1 figure

The effective field theory (EFT) of inflation has become the preferred method for computing cosmological correlation functions of the curvature fluctuation, $\zeta$. It makes explicit use of the soft breaking of time diffeomorphisms by the inflationary background to organize the operators expansion in the action of the Goldstone mode $\pi$ associated with this breaking. Despite its ascendancy, there is another method for calculating $\zeta$ correlators, involving the direct calculation of the so-called Horndeski action order by order in powers of $\zeta$ and its derivatives. The question we address in this work is whether or not the $\zeta$ correlators calculated in these seemingly different ways are in fact the same. The answer is that the actions to cubic order in either set of variables do indeed give rise to the same $\zeta$ bispectra, but that to make this equivalence manifest requires a careful understanding of the non-linear transformations relating $\pi$ to $\zeta$ and how boundary terms in the actions are affected by imposing this relation. As a by product of our study we find that the calculations in the $\pi$ language can be simplified considerably in a way that allows us to use only the linear part of the $\pi-\zeta$ relation simply by changing the coefficients of some of the operators in the EFT. We also note that a proper accounting of the boundary terms will be of the greatest importance when computing the bispectrum for more general initial states than the Bunch-Davies one., Comment: v1: 20 pages, 1 figure. v2: references and minor clarifications added, results remain unchanged; matches version to be published in JCAP

We compute the one-loop quantum corrections to the potential of ghost-free massive gravity. We show how the mass of external matter fields contribute to the running of the cosmological constant, but do not change the ghost-free structure of the massive gravity potential at one-loop. When considering gravitons running in the loops, we show how the structure of the potential gets destabilized at the quantum level, but in a way which would never involve a ghost with a mass smaller than the Planck scale. This is done by explicitly computing the one-loop effective action and supplementing it with the Vainshtein mechanism. We conclude that to one-loop order the special mass structure of ghost-free massive gravity is technically natural., Comment: v2: References added, 29 pages, 7 figures

We provide a formula for the scaling behaviour of the inflationary bispectrum in the 'squeezed' limit where one momentum becomes much smaller than the other two. This determines the scaling of the halo bias at low wavenumber and will be an important observable for the next generation of galaxy surveys. Our formula allows it to be predicted for the first time for a generic inflationary model with multiple light, canonically-normalized scalar fields., Comment: 5 pages, 1 figure

The effective field theory (EFT) of inflation has become the preferred method for computing cosmological correlation functions of the curvature fluctuation, $\zeta$. It makes explicit use of the soft breaking of time diffeomorphisms by the inflationary background to organize the operators expansion in the action of the Goldstone mode $\pi$ associated with this breaking. Despite its ascendancy, there is another method for calculating $\zeta$ correlators, involving the direct calculation of the so-called Horndeski action order by order in powers of $\zeta$ and its derivatives. The question we address in this work is whether or not the $\zeta$ correlators calculated in these seemingly different ways are in fact the same. The answer is that the actions to cubic order in either set of variables do indeed give rise to the same $\zeta$ bispectra, but that to make this equivalence manifest requires a careful understanding of the non-linear transformations relating $\pi$ to $\zeta$ and how boundary terms in the actions are affected by imposing this relation. As a by product of our study we find that the calculations in the $\pi$ language can be simplified considerably in a way that allows us to use only the linear part of the $\pi-\zeta$ relation simply by changing the coefficients of some of the operators in the EFT. We also note that a proper accounting of the boundary terms will be of the greatest importance when computing the bispectrum for more general initial states than the Bunch-Davies one., Comment: v1: 20 pages, 1 figure. v2: references and minor clarifications added, results remain unchanged; matches version to be published in JCAP

Until recently our knowledge of the primordial curvature perturbation was relatively modest. Ever since COBE delivered its map of data we know the scalar spectrum of primordial perturbations is approximately flat, with the power being only slightly stronger at larger scales. Most inflationary models predict an approximately scale-invariant spectrum, which therefore cannot be used as a distinctive signature. To distinguish between different inflationary microphysics we need to study higher point statistics of the primordial perturbation, which can encode non-gaussian data. In the first part of this thesis we study the bispectrum in all single-field models with a well-defined quantum field theory during a quasi-de Sitter inflationary phase. Any single-field models without ghost-like instabilities fall into this description: from canonical, to Dirac-Born-Infeld inflation and galileon inflation theories. We investigate the scale and shape- dependences of the bispectrum to next-order in the slow-roll approximation. We illustrate our results by applying them to different models and argue these corrections must be taken into account to keep the theoretical error below the observational precision set by the Planck satellite. We then explore the ability of using bispectrum shapes to distinguish between inflationary models more efficiently. We further extend the study of the bispectrum of single-field models beyond the slow-roll approximation, demanding the spectral index to be close to, but not exactly, unity. In the second part of this thesis we explore the process by which the universe is repopulated with matter particles at the end of a Dirac-Born-Infeld inflation phase. We place some mild bounds on the reheating temperature of these models. We argue that the constraints arising from the preheating analysis are complementary to those derived from the primordial perturbation., Comment: PhD thesis, 253 pages

We compute the one-loop quantum corrections to the potential of ghost-free massive gravity. We show how the mass of external matter fields contribute to the running of the cosmological constant, but do not change the ghost-free structure of the massive gravity potential at one-loop. When considering gravitons running in the loops, we show how the structure of the potential gets destabilized at the quantum level, but in a way which would never involve a ghost with a mass smaller than the Planck scale. This is done by explicitly computing the one-loop effective action and supplementing it with the Vainshtein mechanism. We conclude that to one-loop order the special mass structure of ghost-free massive gravity is technically natural., Comment: v2: References added, 29 pages, 7 figures

We present the first 3+1-dimensional numerical simulations of scalar fields with non-minimal kinetic terms. As an example, we examine the existence and stability of preheating in the presence of a Dirac-Born-Infeld (DBI) inflaton coupled to a canonical matter field. The simulations represent the full non-linear theory in the presence of an expanding Universe. We show that parametric resonance in the matter field, along with self-resonance in the inflaton, repopulate the Universe with matter particles as efficiently as in traditional preheating., Comment: 5 pages, 3 figures; note correction to parameter value in first paragraph of Numerical Simulations section (typographical error in published version)

We provide a formula for the scaling behaviour of the inflationary bispectrum in the 'squeezed' limit where one momentum becomes much smaller than the other two. This determines the scaling of the halo bias at low wavenumber and will be an important observable for the next generation of galaxy surveys. Our formula allows it to be predicted for the first time for a generic inflationary model with multiple light, canonically-normalized scalar fields., Comment: 5 pages, 1 figure

The effective field theory (EFT) of inflation has become the preferred method for computing cosmological correlation functions of the curvature fluctuation, $\zeta$. It makes explicit use of the soft breaking of time diffeomorphisms by the inflationary background to organize the operators expansion in the action of the Goldstone mode $\pi$ associated with this breaking. Despite its ascendancy, there is another method for calculating $\zeta$ correlators, involving the direct calculation of the so-called Horndeski action order by order in powers of $\zeta$ and its derivatives. The question we address in this work is whether or not the $\zeta$ correlators calculated in these seemingly different ways are in fact the same. The answer is that the actions to cubic order in either set of variables do indeed give rise to the same $\zeta$ bispectra, but that to make this equivalence manifest requires a careful understanding of the non-linear transformations relating $\pi$ to $\zeta$ and how boundary terms in the actions are affected by imposing this relation. As a by product of our study we find that the calculations in the $\pi$ language can be simplified considerably in a way that allows us to use only the linear part of the $\pi-\zeta$ relation simply by changing the coefficients of some of the operators in the EFT. We also note that a proper accounting of the boundary terms will be of the greatest importance when computing the bispectrum for more general initial states than the Bunch-Davies one., Comment: v1: 20 pages, 1 figure. v2: references and minor clarifications added, results remain unchanged; matches version to be published in JCAP

Until recently our knowledge of the primordial curvature perturbation was relatively modest. Ever since COBE delivered its map of data we know the scalar spectrum of primordial perturbations is approximately flat, with the power being only slightly stronger at larger scales. Most inflationary models predict an approximately scale-invariant spectrum, which therefore cannot be used as a distinctive signature. To distinguish between different inflationary microphysics we need to study higher point statistics of the primordial perturbation, which can encode non-gaussian data. In the first part of this thesis we study the bispectrum in all single-field models with a well-defined quantum field theory during a quasi-de Sitter inflationary phase. Any single-field models without ghost-like instabilities fall into this description: from canonical, to Dirac-Born-Infeld inflation and galileon inflation theories. We investigate the scale and shape- dependences of the bispectrum to next-order in the slow-roll approximation. We illustrate our results by applying them to different models and argue these corrections must be taken into account to keep the theoretical error below the observational precision set by the Planck satellite. We then explore the ability of using bispectrum shapes to distinguish between inflationary models more efficiently. We further extend the study of the bispectrum of single-field models beyond the slow-roll approximation, demanding the spectral index to be close to, but not exactly, unity. In the second part of this thesis we explore the process by which the universe is repopulated with matter particles at the end of a Dirac-Born-Infeld inflation phase. We place some mild bounds on the reheating temperature of these models. We argue that the constraints arising from the preheating analysis are complementary to those derived from the primordial perturbation., Comment: PhD thesis, 253 pages

We compute the one-loop quantum corrections to the potential of ghost-free massive gravity. We show how the mass of external matter fields contribute to the running of the cosmological constant, but do not change the ghost-free structure of the massive gravity potential at one-loop. When considering gravitons running in the loops, we show how the structure of the potential gets destabilized at the quantum level, but in a way which would never involve a ghost with a mass smaller than the Planck scale. This is done by explicitly computing the one-loop effective action and supplementing it with the Vainshtein mechanism. We conclude that to one-loop order the special mass structure of ghost-free massive gravity is technically natural., Comment: v2: References added, 29 pages, 7 figures

We present the first 3+1-dimensional numerical simulations of scalar fields with non-minimal kinetic terms. As an example, we examine the existence and stability of preheating in the presence of a Dirac-Born-Infeld (DBI) inflaton coupled to a canonical matter field. The simulations represent the full non-linear theory in the presence of an expanding Universe. We show that parametric resonance in the matter field, along with self-resonance in the inflaton, repopulate the Universe with matter particles as efficiently as in traditional preheating., Comment: 5 pages, 3 figures; note correction to parameter value in first paragraph of Numerical Simulations section (typographical error in published version)

We provide a formula for the scaling behaviour of the inflationary bispectrum in the 'squeezed' limit where one momentum becomes much smaller than the other two. This determines the scaling of the halo bias at low wavenumber and will be an important observable for the next generation of galaxy surveys. Our formula allows it to be predicted for the first time for a generic inflationary model with multiple light, canonically-normalized scalar fields., Comment: 5 pages, 1 figure

We derive the 'separate universe' method for the inflationary bispectrum, beginning directly from a field-theory calculation. We work to tree-level in quantum effects but to all orders in the slow-roll expansion, with masses accommodated perturbatively. Our method provides a systematic basis to account for novel sources of time-dependence in inflationary correlation functions, and has immediate applications. First, we use our result to obtain the correct matching prescription between the 'quantum' and 'classical' parts of the separate universe computation. Second, we elaborate on the application of this method in situations where its validity is not clear. As a by-product of our calculation we give the leading slow-roll corrections to the three-point function of field fluctuations on spatially flat hypersurfaces in a canonical, multiple-field model., Comment: v1: 33 pages, plus appendix and references; 5 figures. v2: typographical typos fixed, minor changes to the main text and abstract, reference added; matches version published in JCAP

If the expansion of the early Universe was not close to de Sitter, the statistical imprints of the primordial density perturbation on the cosmic microwave background can be quite different from those derived in slow-roll inflation. In this paper we study the inflationary signatures of all single-field models which are free of ghost-like instabilities. We allow for a rapid change of the Hubble parameter and the speed of sound of scalar fluctuations, in a way that is compatible with a nearly scale-invariant spectrum of perturbations, as supported by current cosmological observations. Our results rely on the scale-invariant approximation, which is different from the standard slow-roll approximation. We obtain the propagator of scalar fluctuations and compute the bispectrum, keeping next-order corrections proportional to the deviation of the spectral index from unity. These theories offer an explicit example where the shape and scale-dependences of the bispectrum are highly non-trivial whenever slow-roll is not a good approximation., Comment: v1: 36 pages, including tables, appendices and references. v2: abstract improved, references added, minor clarifications throughout the text; matches version published in JCAP

A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "delta N" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, zeta, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform energy-density hypersurfaces in field space., Comment: 22 pages, plus bibliography and appendix. v2: minor changes, matches version published in JCAP

A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "delta N" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, zeta, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform energy-density hypersurfaces in field space., Comment: 22 pages, plus bibliography and appendix. v2: minor changes, matches version published in JCAP

If the expansion of the early Universe was not close to de Sitter, the statistical imprints of the primordial density perturbation on the cosmic microwave background can be quite different from those derived in slow-roll inflation. In this paper we study the inflationary signatures of all single-field models which are free of ghost-like instabilities. We allow for a rapid change of the Hubble parameter and the speed of sound of scalar fluctuations, in a way that is compatible with a nearly scale-invariant spectrum of perturbations, as supported by current cosmological observations. Our results rely on the scale-invariant approximation, which is different from the standard slow-roll approximation. We obtain the propagator of scalar fluctuations and compute the bispectrum, keeping next-order corrections proportional to the deviation of the spectral index from unity. These theories offer an explicit example where the shape and scale-dependences of the bispectrum are highly non-trivial whenever slow-roll is not a good approximation., Comment: v1: 36 pages, including tables, appendices and references. v2: abstract improved, references added, minor clarifications throughout the text; matches version published in JCAP