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In this review, a pedagogical introduction to the concepts of slow-roll inflationary universe and number of e-folds is provided. In particular, the differences between the basic notion of number of e-folds ( N e ), total number of e-folds ( N T ) and number of e-folds before the end of inflation (N) are outlined. The proper application of the number of e-folds before the end of inflation is discussed both as a time-like variable for the scalar field evolution and as a key parameter for computing inflationary predictions. [ABSTRACT FROM AUTHOR]

We review applications of string theory to cosmology, from primordial times to the present-day accelerated expansion. Starting with a brief overview of cosmology and string compactifications, we discuss in detail moduli stabilisation, inflation in string theory, the impact of string theory on post-inflationary dynamics (reheating, moduli domination, kination), dark energy (the cosmological constant from a string landscape and models of quintessence) and various alternative scenarios (string/brane gases, the pre big-bang scenario, rolling tachyons, ekpyrotic/cyclic cosmologies, bubbles of nothing, S-brane and holographic cosmologies). The state of the art in string constructions is described in each topic and, where relevant, connections to swampland conjectures are made. The possibilities for novel particles and excitations (axions, moduli, cosmic strings, branes, solitons, oscillons and boson stars) are emphasised. Implications for the physics of the CMB, gravitational waves, dark matter and dark radiation are discussed along with potential observational signatures. [ABSTRACT FROM AUTHOR]

In this review, a pedagogical introduction to the concepts of slow-roll inflationary universe and number of e-folds is provided. In particular, the differences between the basic notion of number of e-folds (Ne), total number of e-folds (NT) and number of e-folds before the end of inflation (N) are outlined. The proper application of the number of e-folds before the end of inflation is discussed both as a time-like variable for the scalar field evolution and as a key parameter for computing inflationary predictions.

The Big Bang singularity in standard model cosmology suggests a program of study in ‘early universe’ quantum gravity phenomenology. Inflation is usually thought to undermine this program’s prospects by means of a dynamical diluting argument, but such a view has recently been disputed within inflationary cosmology, in the form of a ‘trans-Planckian censorship’ conjecture. Meanwhile, trans-Planckian censorship has been used outside of inflationary cosmology to motivate alternative early universe scenarios that are tightly linked to ongoing theorizing in quantum gravity. Against the resulting trend toward early universe quantum gravity phenomenology within and without inflation, Ijjas and Steindhardt suggest a further alternative: a ‘generalized cosmic censorship’ principle. I contrast the generalized cosmic censorship principle with the logic of its namesake, the cosmic censorship conjectures. I also remark on foundational concerns in the effective field theory approach to cosmology beyond the standard model, which would be based on that principle. [ABSTRACT FROM AUTHOR]

Warm inflation has normalized two ideas in cosmology, that in the early universe the initial primordial density perturbations generally could be of classical rather than quantum origin and that during inflation, particle production from interactions amongst quantum field, and its backreaction effects, can occur concurrent with inflationary expansion. When we first introduced these ideas, both were met with resistance, but today they are widely accepted as possibilities with many models and applications based on them, which is an indication of the widespread influence of warm inflation. Open quantum field theory, which has been utilized in studies of warm inflation, is by now a relevant subject in cosmology, in part due to this early work. In this review I first discuss the basic warm inflation dynamics. I then outline how to compute warm inflation dynamics from first-principles quantum field theory (QFT) and in particular how a dissipative term arises. Warm inflation models can have an inflaton mass bigger than the Hubble scale and the inflaton field excursion can remain sub-Planckian, thus overcoming the most prohibitive problems of inflation model building. I discuss the early period of my work in developing warm inflation that helped me arrive at these important features of its dynamics. Inflationary cosmology today is immersed in hypothetical models, which by now are acting as a diversion from reaching any endgame in this field. I discuss better ways to approach model selection and give necessary requirements for a well constrained and predictive inflation model. A few warm inflation models are pointed out that could be developed to this extent. I discuss how, at this stage, more progress would be made in this subject by taking a broader view on the possible early universe solutions that include not just inflation but the diverse range of options. [ABSTRACT FROM AUTHOR]

Warm inflation has normalized two ideas in cosmology, that in the early universe the initial primordial density perturbations generally could be of classical rather than quantum origin and that during inflation, particle production from interactions amongst quantum field, and its backreaction effects, can occur concurrent with inflationary expansion. When we first introduced these ideas, both were met with resistance, but today they are widely accepted as possibilities with many models and applications based on them, which is an indication of the widespread influence of warm inflation. Open quantum field theory, which has been utilized in studies of warm inflation, is by now a relevant subject in cosmology, in part due to this early work. In this review I first discuss the basic warm inflation dynamics. I then outline how to compute warm inflation dynamics from first-principles quantum field theory (QFT) and in particular how a dissipative term arises. Warm inflation models can have an inflaton mass bigger than the Hubble scale and the inflaton field excursion can remain sub-Planckian, thus overcoming the most prohibitive problems of inflation model building. I discuss the early period of my work in developing warm inflation that helped me arrive at these important features of its dynamics. Inflationary cosmology today is immersed in hypothetical models, which by now are acting as a diversion from reaching any endgame in this field. I discuss better ways to approach model selection and give necessary requirements for a well constrained and predictive inflation model. A few warm inflation models are pointed out that could be developed to this extent. I discuss how, at this stage, more progress would be made in this subject by taking a broader view on the possible early universe solutions that include not just inflation but the diverse range of options.

We discuss the production of radiation and dark matter assuming a time-dependent inflaton decay rate during the reheating period. It is shown that the time dependence of the inflaton decay rate can substantially modify the reheating dynamics. As an illustration, a leading interaction between the inflaton ϕ and the Higgs doublet h of the form ϕ|h|2 was adopted. In the presence of such interaction, the Higgs doublet acquires a ϕ-dependent mass which generates vacuum-expectation-value due to inflaton oscillations and breaks the Standard Model gauge symmetry. This leads to a time-dependent inflaton decay rate during the reheating period, and consequently, the production of radiation and dark matter during this period is modified. Regions of the parameter space that describe the observed value of the dark matter abundance were found and compared with the standard case when inflaton the decay rate is constant.

The theory of cosmic inflation has received a great amount of deserved attention in recent years due to it's stunning predictions about the early universe. Alongside the usual cold inflation paradigm, warm inflation has garnered a huge amount of interest in modern inflationary studies. It's peculiar features and specifically different predictions from cold inflation have led to a substantial amount of literature about it. Various modified cosmological scenarios have also been studied in the warm inflationary regime. In this work, we introduce the exact solution approach for warm inflation. This approach allows one to directly study warm inflationary regime in a variety of modified cosmological scenarios. We begin by outlining our method and show that it generalizes the modified Friedmann approach of Del Campo, and reduces to the well known Hamilton–Jacobi formalism for inflation in particular limits. We also find the perturbation spectra for cosmological and tensor perturbations in the early universe, and then apply our method to study warm inflation in a Tsallis entropy modified Friedmann universe. We end our paper with some concluding remarks on the domain of applicability of our work. [ABSTRACT FROM AUTHOR]

I provide some philosophical groundwork for the recently proposed 'trans-Planckian censorship' conjecture in theoretical physics. In particular, I argue that structure formation in early universe cosmology is, at least as we typically understand it, autonomous with regards to quantum gravity, the high energy physics that governs the Planck regime in our universe. Trans-Planckian censorship is then seen as a means of rendering this autonomy an empirical constraint within ongoing quantum gravity research. [ABSTRACT FROM AUTHOR]

TheWeyl curvature constitutes the radiative sector of the Riemann curvature tensor and gives a measure of the anisotropy and inhomogeneities of spacetime. Penrose's 1979 Weyl curvature hypothesis (WCH) assumes that the universe began at a very low gravitational entropy state, corresponding to zero Weyl curvature, namely, the Friedmann--Lemaître--Robertson--Walker (FLRW) universe. This is a simple assumption with far-reaching implications. In classical general relativity, Belinsky, Khalatnikov and Lifshitz (BKL) showed in the 70s that the most general cosmological solutions of the Einstein equation are that of the inhomogeneous Kasner types, with intermittent alteration of the one direction of contraction (in the cosmological expansion phase), according to the mixmaster dynamics of Misner (M). How could WCH and BKL-M co-exist? An answer was provided in the 80s with the consideration of quantum field processes such as vacuum particle creation, which was copious at the Planck time (10-43s), and their backreaction effects were shown to be so powerful as to rapidly damp away the irregularities in the geometry. It was proposed that the vaccum viscosity due to particle creation can act as an efficient transducer of gravitational entropy (large for BKL-M) to matter entropy, keeping the universe at that very early time in a state commensurate with the WCH. In this essay I expand the scope of that inquiry to a broader range, asking how the WCH would fare with various cosmological theories, from classical to semiclassical to quantum, focusing on their predictions near the cosmological singularities (past and future) or avoidance thereof, allowing the Universe to encounter different scenarios, such as undergoing a phase transition or a bounce. WCH is of special importance to cyclic cosmologies, because any slight irregularity toward the end of one cycle will generate greater anisotropy and inhomogeneities in the next cycle. We point out that regardless of what other processes may be present near the beginning and the end states of the universe, the backreaction effects of quantum field processes probably serve as the best guarantor of WCH because these vacuum processes are ubiquitous, powerful and efficient in dissipating the irregularities to effectively nudge the Universe to a near-zeroWeyl curvature condition. [ABSTRACT FROM AUTHOR]

I review the Trans-Planckian Censorship Conjecture (TCC) and its implications for cosmology, in particular for the inflationary universe scenario. Whereas the inflationary scenario is tightly constrained by the TCC, alternative early universe scenarios are not restricted.

Primordial black holes, which could have been formed in the very early Universe due to the collapse of large curvature fluctuations, are currently one of the most attractive and fascinating research areas in cosmology for their possible theoretical and observational implications. This review article presents the current results and developments on the conditions for primordial black hole formation from the collapse of curvature fluctuations in spherical symmetry on a Friedman–Lemaître–Robertson–Walker background and its numerical simulation. We review the appropriate formalism for the conditions of primordial black hole formation, and we detail a numerical implementation. We then focus on different results regarding the threshold and the black hole mass using different sets of curvature fluctuations. Finally, we present the current state of analytical estimations for the primordial black hole formation threshold, contrasted with numerical simulations.

Primordial magnetic field generated in the inflationary era can act as a viable source for the present day intergalactic magnetic field of sufficient strength. We present a fundamental origin for such a primordial generation of the magnetic field, namely through anomaly cancellation of U(1) gauge field in quantum electrodynamics in the context of hilltop inflation. We have analysed at length the power spectrum of the magnetic field, thus generated, which turns out to be helical in nature. We have also found that magnetic power spectrum has significant scale-dependence giving rise to a non-trivial magnetic spectral index, a key feature of this model. Interestingly, there exists a large parameter space, where magnetic field of significant strength can be produced.

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra gu that extends e9. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn gu into a Lie superalgebra sgu with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincaré group on sgu, which is an automorphism in the massive sector. We introduce a mechanism for scattering that includes decays as particular resonant scattering. Finally, we complete the model by merging the local sgu into a vertex-type algebra.

We introduce a quantum model for the universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the Kac–Moody Lie algebra e9. We investigate Kac–Moody and Borcherds algebras, and we propose a generalization that meets further requirements that we regard as fundamental in quantum gravity.

We study various production mechanisms of sterile neutrinos in the early universe beyond and within the standard model. We obtain the quantum kinetic equations for production and the distribution function of sterile-like neutrinos at freeze-out, from which we obtain free streaming lengths, equations of state and coarse grained phase space densities. In a simple extension beyond the standard model, in which neutrinos are Yukawa coupled to a Higgs-like scalar, we derive and solve the quantum kinetic equation for sterile production and analyze the freeze-out conditions and clustering properties of this dark matter constituent. We argue that in the mass basis, standard model processes that produce active neutrinos also yield sterile-like neutrinos, leading to various possible production channels. Hence, the final distribution function of sterile-like neutrinos is a result of the various kinematically allowed production processes in the early universe. As an explicit example, we consider production of light sterile neutrinos from pion decay after the QCD phase transition, obtaining the quantum kinetic equation and the distribution function at freeze-out. A sterile-like neutrino with a mass in the keV range produced by this process is a suitable warm dark matter candidate with a free-streaming length of the order of few kpc consistent with cores in dwarf galaxies.

In this work, we present some cosmologically relevant solutions using the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in metric f ( R ) gravity where the form of the gravitational Lagrangian is given by 1 α e α R . In the low curvature limit this theory reduces to ordinary Einstein-Hilbert Lagrangian together with a cosmological constant term. Precisely because of this cosmological constant term this theory of gravity is able to support nonsingular bouncing solutions in both matter and vacuum background. Since for this theory of gravity f ′ and f ″ is always positive, this is free of both ghost instability and tachyonic instability. Moreover, because of the existence of the cosmological constant term, this gravity theory also admits a de-Sitter solution. Lastly we hint towards the possibility of a new type of cosmological solution that is possible only in higher derivative theories of gravity like this one.

Recent analyses of cosmic microwave background surveys have revealed hints that there may be a non-trivial running of the running of the spectral index. If future experiments were to confirm these hints, it would prove a powerful discriminator of inflationary models, ruling out simple single field models. We discuss how isocurvature perturbations in multi-field models can be invoked to generate large runnings in a non-standard hierarchy, and find that a minimal model capable of practically realising this would be a two-field model with a non-canonical kinetic structure. We also consider alternative scenarios such as variable speed-of-light models and canonical quantum gravity effects and their implications for runnings of the spectral index.

We discuss the production of radiation and dark matter assuming a time-dependent inflaton decay rate during the reheating period. It is shown that the time dependence of the inflaton decay rate can substantially modify the reheating dynamics. As an illustration, a leading interaction between the inflaton ϕ and the Higgs doublet h of the form ϕ | h | 2 was adopted. In the presence of such interaction, the Higgs doublet acquires a ϕ -dependent mass which generates vacuum-expectation-value due to inflaton oscillations and breaks the Standard Model gauge symmetry. This leads to a time-dependent inflaton decay rate during the reheating period, and consequently, the production of radiation and dark matter during this period is modified. Regions of the parameter space that describe the observed value of the dark matter abundance were found and compared with the standard case when inflaton the decay rate is constant. [ABSTRACT FROM AUTHOR]

We investigate the idea that the universe before the Big Bang is the C P T reflection of the universe after the bang, both classically and quantum mechanically, so that the universe does not spontaneously violate C P T. We show how C P T symmetry selects a preferred vacuum state for quantum fields on a C P T -invariant cosmological background spacetime. The universe before the bang and the universe after the bang may be viewed as a universe/anti-universe pair, emerging directly into the hot, radiation-dominated era we observe in our past. This, in turn, leads to a remarkably economical explanation of the cosmological dark matter. With no additional fields beyond Einstein gravity and the standard model of particle physics (including right-handed neutrinos), a Z 2 symmetry stabilizes one of the right-handed neutrinos. We calculate its abundance in detail and show that, in order to match the observed dark matter density, its mass must be 4. 8 × 1 0 8 GeV. We obtain several further predictions, including: (i) that the three light neutrinos are majorana; (ii) that one of these is exactly massless; and (iii) that, in the absence of an epoch of cosmic inflation, there should be no primordial, long-wavelength gravitational waves. We also briefly discuss the natural origin of the matter–antimatter asymmetry within this picture and possibilities for explaining the cosmological perturbations. • We suggest the universe before the Big Bang is the "anti-verse" of the universe after the Big Bang. • Thus the universe as a whole is CPT symmetric. • This model gives an elegant and testable new explanation for the dark matter. • Dark matter is a sterile neutrino, radiated from the Bang like Hawking radiation from a black hole. • The model explains/predicts several observable properties of the primordial perturbations. [ABSTRACT FROM AUTHOR]

The Friedman-Robertson-Walker (FRW) spacetime exhibits particle creation similar to Hawking radiation of a black hole. In this essay we show that this FRW Hawking radiation leads to an effective negative pressure fluid which can drive an inflationary period of exponential expansion in the early universe. Since the Hawking temperature of the FRW spacetime decreases as the universe expands this mechanism naturally turns off and the inflationary stage transitions to a power law expansion associated with an ordinary radiation-dominated universe. [ABSTRACT FROM AUTHOR]

Reheating is an important part of inflationary cosmology. It describes the production of Standard Model particles after the phase of accelerated expansion. We review the reheating process with a focus on an in-depth discussion of the preheating stage, which is characterized by exponential particle production due to a parametric resonance or tachyonic instability. We give a brief overview of the thermalization process after preheating and end with a survey of some applications to supersymmetric theories and to other issues in cosmology, such as baryogenesis, dark matter, and metric preheating. [ABSTRACT FROM AUTHOR]

Primordial black holes, which could have been formed in the very early Universe due to the collapse of large curvature fluctuations, are currently one of the most attractive and fascinating research areas in cosmology for their possible theoretical and observational implications. This review article presents the current results and developments on the conditions for primordial black hole formation from the collapse of curvature fluctuations in spherical symmetry on a Friedman–Lemaître–Robertson–Walker background and its numerical simulation. We review the appropriate formalism for the conditions of primordial black hole formation, and we detail a numerical implementation. We then focus on different results regarding the threshold and the black hole mass using different sets of curvature fluctuations. Finally, we present the current state of analytical estimations for the primordial black hole formation threshold, contrasted with numerical simulations. [ABSTRACT FROM AUTHOR]

Primordial magnetic field generated in the inflationary era can act as a viable source for the present day intergalactic magnetic field of sufficient strength. We present a fundamental origin for such a primordial generation of the magnetic field, namely through anomaly cancellation of U (1) gauge field in quantum electrodynamics in the context of hilltop inflation. We have analysed at length the power spectrum of the magnetic field, thus generated, which turns out to be helical in nature. We have also found that magnetic power spectrum has significant scale-dependence giving rise to a non-trivial magnetic spectral index, a key feature of this model. Interestingly, there exists a large parameter space, where magnetic field of significant strength can be produced. [ABSTRACT FROM AUTHOR]

We introduce a quantum model for the universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the Kac–Moody Lie algebra e 9 . We investigate Kac–Moody and Borcherds algebras, and we propose a generalization that meets further requirements that we regard as fundamental in quantum gravity. [ABSTRACT FROM AUTHOR]

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra g u that extends e 9 . It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn g u into a Lie superalgebra sg u with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincaré group on sg u , which is an automorphism in the massive sector. We introduce a mechanism for scattering that includes decays as particular resonant scattering. Finally, we complete the model by merging the local sg u into a vertex-type algebra. [ABSTRACT FROM AUTHOR]

Recent studies suggest that the process of symmetry breaking after inflation typically occurs very fast, within a single oscillation of the symmetry-breaking field, due to the spinodal growth of its long-wave modes, otherwise known as ‘tachyonic preheating’. We show how this sudden transition from the false to the true vacuum can induce a significant production of particles, bosons and fermions, coupled to the symmetry-breaking field. We find that this new mechanism of particle production in the early Universe may have interesting consequences for the origin of dark matter and the generation of the observed baryon asymmetry through leptogenesis. [Copyright &y& Elsevier]