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We have deduced that bulk viscous Bianchi type I barotropic fluid cosmological model with varying $\Lambda$ and functional relation on hubble parameter by solving the field equations bimetric theory of gravitation. It is observed that our model has exponentially accelerating expansion at late time starting with decelerating expansion which agreed the observation of Perlmutter (1998), Knop (2003), Tegmark (2004) and Spergel (2006). In the beginning, our model has more than three spatial-dimensions then it switched over to three-dimensional spatial geometry at late epoch of time and it is agreed with Borkar et al. (2013). Other geometrical and physical behavior of the model have been studied.

For more than a century, Einstein's theory of general relativity has described gravitational phenomena with astonishing precision. However, for the theory to fit observations we need to add two elusive substances: dark energy and dark matter. Together they add up to 95% of the energy budget of the Universe. Yet, we do not know what these substances are. Another question mark is the expansion rate of the Universe; two incompatible values are obtained depending on the measuring method. These problems (dark energy, dark matter, and the expansion rate) belong to the big questions within gravity today and they may be interpreted as signs that general relativity is not the final theory for gravity. As an alternative, in this thesis we analyze an extended theory of gravity called bimetric gravity. In general relativity (GR), gravity is massless which means that gravitational waves propagate at the speed of light. Hence, a natural extension is to consider theories where gravity has a mass. This is precisely what bimetric gravity achieves. The theoretical consistency of this theory is firmly established but it is also crucial to test if the theory agrees with observations. In fact, in this theory there are two types of gravitational waves/fields, one massless as in GR but also one massive. When observing gravitational phenomena, we observe a mix of the two. Depending on the mixing and on the mass of the massive field, observational signatures appear for example on cosmological scales, in gravitational wave events or on solar-system scales. Until recently the phenomenology of the full theory was still uncharted, and an important question was if all observational tests could be satisfied at the same time. To address this, we devised a unified framework that enables straightforward comparison between constraints from different probes, without being restricted to a particular region of the parameter space. The result is that bimetric gravity is compatible with observations and even fit data slightly better than GR. Together with the fact that the dark energy can be explained by the interaction between the two gravitational fields, we have shown that the theory is a viable dark energy candidate. At the same time, the observational data provides a substantial restriction on the parameter space that excludes many of the popular models in the literature – an important result in and of itself. A longstanding issue within this theory has been to predict the growth of structure while avoiding exponential instabilities. Here, we propose a simple model which solves the full, nonlinear equations of motion, which can be used to calculate the growth of structure, without any instabilities. We also describe our work towards a framework for calculating the process of gravitational collapse in this theory where we manage to solve the equations numerically for a short time interval. The results indicate that the gravitational collapse proceeds as in general relativity, assuming that the initial conditions are similar. Future work is needed to decide whether bimetric gravity can solve any of the other big questions within gravity today, such as the discrepant expansion rate of the Universe. In this thesis, we show that it is an observationally viable dark energy candidate that exhibits novel gravitational features. In short, gravity can be massive.

Bimetric gravity theories describes gravitational interactions in the presence of an extra spin-2 field. The Hassan-Rosen (HR) nonlinear massive minimal bigravity theory is a ghost-free bimetric theory formulated with respect a flat, dynamical reference metric. In this work the deformation quantization formalism is applied to a HR cosmological model in the minisuperspace. The quantization procedure is performed explicitly for quantum cosmology in the minisuperspace. The Friedmann-Lema\^itre-Robertson-Walker (FLRW) model with flat metrics is worked out and the computation of the Wigner functions for theHartle-Hawking, Vilenkin and Linde wavefunctions are done numerically and, in the Hartle-Hawking case, also analytically. From the stability analysis in the quantum minisuper phase space it is found an interpretation of the mass of graviton as an emergent cosmological constant and as a measure of the deviation of classical behavior of the Wigner functions. Also, from the Hartle-Hawking case, an interesting relation between the curvature and the mass of graviton in a cusp catastrophe surface is discussed, Comment: This is a post-peer-review, pre-copyedit version of an article published in General Relativity and Gravitation. The final authenticated version is available online at: https://doi.org/10.1007/s10714-021-02822-2 25 pages, 10 figures

I compare two holographic mechanisms giving to the graviton a parametrically-small supersymmetric mass $m_g$ in Anti-de Sitter spacetime. In the context of bi-metric gravity these mechanisms couple `weakly' two initially decoupled superconformal theories by: (i) turning on a double-trace deformation, or (ii) gauging a common global symmetry. Superconformal invariance restricts the number of Poincar\'e supercharges to $N_Q\leq 4$ for mechanism (i) and to $N_Q\leq 8$ for mechanism (ii), and the AdS dimension to $D\leq 5$. The putative effective supergravities are expected to break down in the $m_g\to 0$ limit at an intermediate scale between $ m_g$ and $m_{\rm Planck}$. In a recently-proposed microscopic embedding of mechanism (ii) in string theory I show that $m_g=0$ is at infinite distance in moduli space, and I relate the breakdown of the effective theory to the condensation of unprotected spin-2 excitations in the string-theoretic description of the `holographic bridge'. The phenomenon is invisible in the weakly-coupled CFT side. I conjecture that similar phenomena should be at work in all cases., Comment: 19 pages, one figure. Minor corrections and amendments. Version to be published in JHEP

We consider a 5-dimensional Chern-Simons gauge theory for the isometry group of Anti-de-Sitter spacetime, $\operatorname{AdS}_{4+1}\simeq\operatorname{SO}(4,2)$, and invoke different dimensional reduction schemes in order to relate it to 4-dimensional spin-2 theories. The AdS gauge algebra is isomorphic to a parametrized 4-dimensional conformal algebra, and the gauge fields corresponding to the generators of non-Abelian translations and special conformal transformations reduce to two vierbein fields in $D=4$. Besides these two vierbeine, our reduction schemes leave only the Lorentz spin connection as an additional dynamical field in the 4-dimensional theories. We identify the corresponding actions as particular generalizations of Einstein-Cartan theory, conformal gravity and ghost-free bimetric gravity in first-order form., Comment: 31 pages, no figures, added references

Beyond the Standard Theories of Fundamental Interactions. The status quo of fundamental physics is the Standard Model (SM) of particle physics and General Relativity (GR). While both theories separately are able to describe a wide range of phenomena in their respective domain to high accuracy, there are problems which arise solely when the two are coupled. Examples include the cosmological constant problem, baryogenesis or the absence of a suitable dark matter (DM) candidate in the SM. In this thesis, several solutions are presented and discussed. One is Bimetric Gravity, a modification of GR which breaks the assumption that one single, massless spin-2 object acts as its force carrier. Original results are presented on the phenomenology of the massive graviton, where we analyse the modified propagation of gravitational waves and set competitive bounds on the graviton mass. Furthermore, the cosmological history of the model is investigated, incorporating data from baryon acoustic oscillations, quasars, supernovae and the cosmic microwave background. As a competing theory, we review Conformal Gravity, which is put to the same cosmological tests. A complementary approach to the solution of the DM problem is a Dark Sector beyond the SM. We motivate and present a detailed analysis of the physics of Dark Sectors, which obey an approximate scale invariance. Using effective field theory techniques and properties of operators fixed by conformal symmetry, we are able to put model-independent bounds on a class of Dark Sectors. Their phenomenology is tested against a large array of terrestrial and celestial observations. Oltre le Teorie Standard delle Interazioni Fondamentali. Lo status quo della fisica fondamentale è il Modello Standard (SM) e la Relatività Generale (GR). Mentre entrambe le teorie sono in grado di descrivere separatamente una vasta gamma di fenomeni nel loro rispettivo dominio di validità con elevata precisione, ci sono problemi che sorgono solo quando le due sono accoppiate. Come esempio, si consideri il problema della costante cosmologica, la bariogenesi o l’assenza di un candidato di materia oscura (DM) nello SM. In questa tesi vengono presentate e discusse diverse soluzioni. Una è la teoria di Bimetric Gravity, un’estensione naturale della gravità massiva, una modificazione della GR che modifica l’ipotesi di un gravitone di spin-2 senza massa. Saranno presentati risultati sulla fenomenologia del gravitone massivo, dove analizziamo la propagazione modificata delle onde gravitazionali e stabiliamo dei limiti competitivi sulla massa del gravitone. Inoltre, viene studiata la storia cosmologica di Bimetric Gravity, incorporando dati delle oscillazioni acustiche barioniche (BAO), dei quasar, delle supernovae e della radiazione cosmica di fondo. Come teoria concorrente, esaminiamo la Gravità Conforme, che viene sottoposta agli stessi test cosmologici. Un approccio ortogonale alla soluzione del problema della DM è un Settore Oscuro oltre lo SM. Motiviamo e presentiamo un’analisi dettagliata della fisica dei Settori Oscuri, che obbediscono ad un’invarianza approssimativa di scala. Utilizzando tecniche di teoria di campo efficace e proprietà degli operatori fissate dalla simmetria conforme, siamo in grado di porre dei limiti indipendenti dal modello su una classe di Settori Oscuri. La loro fenomenologia è testata con una vasta gamma di osservazioni terrestri e celesti.

The General theory of Relativity was first introduced by Albert Einstein. There have been many attempts to unify General Relativity with the Standard Model of Physics and many of these try to do so by modifying General Relativity slightly. One way to do this is to add a mass to the graviton. Such a theory was proposed by Fierz and Pauli. However, a massive gravity theory suffers from the vDvZ discontinuty where taking the masss of the graviton to zero does not reproduce the results of General Relativity exactly. This can, to some extent, be resolved via the Vainshtein mechanism, where General Relativity can be reproduced within a certain radius from a source, called the Vainshtein radius. Another modification that can be imagined, is to add a second metric. However, doing this results in extra degrees of freedom which manifest as a Boulaware Deser ghost. The bimetric action which avoids the Boulaware Deser ghost was first introduced by Hassan and Rosen in 2011. In this theory, only one of the metrics couples to standard model matter to avoid the ghost. In this scenario, the propagating massless and massive spin-2 modes turn out to be linear combinations of the two metrics, just as in neutrino mixings. In this thesis, we review some works which investigate the oscillations between the massless and massive modes and the implications for gravitational waves. In particular we consider the bounds on the parameters of the theory based on the fact that evidence for such oscillations have not been observed by LIGO. We use a new LIGO result to extend these bounds. We also review an investigation which explores the possibility that the dark matter particle could be the massive particle of bimetric gravity. Den allmänna relativitetsteorin introducerades först av Albert Einstein.Många har försökt förena allmän relativitetsteori med partikelfysikensstandardmodell och många av dessa försök gör detta genom att lägga tillen massa för gravitonen. En sådan teori föreslogs av Fierz och Pauli.Massiv gravitation lider dock av vDvZ-diskontinuiteten där gränsen närgravitonmassan går mot noll inte reproducerar allmän relativitetsteori.Detta kan, till viss del, lösas genom Vainshteinmekanismen, där allmänrelativitetsteori kan reproduceras inom ett visst avstånd från källan,kallat Vainshteinradien. En annan modifikation som kan komma på fråga äratt lägga till en andra metrik. Att göra detta leder dock till nyafrihetsgrader som yttrar sig som ett Boulaware-Deser-spöke. Denbimetriska verkan som undviker Boulaware-Deser-spöket introduceradesförst av Hassan och Rosen år 2011. I denna teori kopplar enbart en avmetrikerna till standardmodellen vilket gör att spöket kan undvikas. Idetta scenario visar sig det masslösa och det massivapropagationsegentillstånden vara linjärkombinationer av de tvåmetrikerna i analogi med neutrinoblandning. I detta arbete går vi igenomnågra arbete som undersöker oscillationerna mellan de två metrikerna ochimplikationerna för gravitationsvågor. Speciellt kommer vi att betraktade begränsningar som finns på teoriparametrarna baserat på det faktumatt LIGO inte observerat några bevis för sådana oscillationer. Vianvänder också nya LIGO-resultat för att utöka dessa begränsningar. Vidiskutera också möjligheten att mörk materia skulle kunna bestå av denmassiva gravitonen i bimetrisk gravitation.

We study spherically symmetric black hole solutions in a four-parameter Einstein-Cartan-type class of theories, called "torsion bigravity". These theories offer a geometric framework (with a metric and an independent torsionfull connection) for a modification of Einstein's theory that has the same spectrum as bimetric gravity models. In addition to an Einsteinlike massless spin-2 excitation, there is a massive spin-2 one (of range $\kappa^{-1}$) coming from the torsion sector, rather than from a second metric. We prove the existence of three broad classes of spherically-symmetric black hole solutions in torsion bigravity. First, the Schwarzschild solution defines an asymptotically-flat torsionless black hole for all values of the parameters. [And we prove that one cannot deform a Schwarzschild solution, at the linearized level, by adding an infinitesimal torsion hair.] Second, when considering finite values of the range, we find that there exist non-asymptotically-flat torsion-hairy black holes in a large domain of parameter space. Third, we find that, in the limit of infinite range, there exists a two-parameter family of asymptotically flat torsion-hairy black holes. The latter black hole solutions give an interesting example of non-Einsteinian (but still purely geometric) black hole structures which might be astrophysically relevant when considering a range of cosmological size., Comment: 19 pages, 3 figures

It was pointed out long ago by Vainshtein [Phys. Lett. 39B, 393 (1972)] that the weak-field perturbation expansion of generic theories (of the nonlinear Fierz-Pauli type) involving massive spin-2 excitations breaks down below a certain distance around a material source ("Vainshtein radius"), scaling as some inverse power of the spin-2 mass $m_2$, i.e., some positive power of the range $m_2^{-1}$. Here we prove that this conclusion does not apply in a generalized Einstein-Cartan theory (called "torsion bigravity") whose spectrum is made (like that of bimetric gravity) of a massless spin-2 excitation and a massive spin-2 one. Working within a static spherically symmetric ansatz, we prove, by reformulating the field equations in terms of new variables, that one can construct an all-order weak-field perturbative expansion where no denominators involving $m_2$ ever appear in the region $r \ll m_2^{-1}$. In particular, we show how the formal large-range limit, $m_2 \to 0$, leads to a well-defined, finite perturbation expansion, whose all-order structure is discussed in some detail., 18 pages, no figures

Bimetric gravity is a ghost-free and observationally viable extension of general relativity, exhibiting both a massless and a massive graviton. The observed abundances of light elements can be used to constrain the expansion history of the Universe at the period of Big Bang nucleosynthesis. Applied to bimetric gravity, we readily obtain constraints on the theory parameters which are complementary to other observational probes. For example, the mixing angle between the two gravitons must satisfy $\theta \lesssim 18^\circ$ in the graviton mass range $m_\mathrm{FP} \gtrsim 10^{-16} \, \mathrm{eV}/c^2$, representing a factor of two improvement compared with other cosmological probes., Comment: 5 pages, v2 minor updates in accordance with the published version. For a short (5 min) video summarizing the main result, see https://youtu.be/uqdbOZQ7k_k

Ghost-free bimetric gravity is a theory of two interacting spin-2 fields, one massless and one massive, in addition to the standard matter particles and fields, thereby generalizing Einstein's theory of general relativity. To parameterize the theory, we use five observables with specific physical interpretations. We present, for the first time, observational constraints on these parameters that: (i) apply to the full theory, (ii) are consistent with a working screening mechanism (i.e., restoring general relativity locally), (iii) exhibit a continuous, real-valued background cosmology (without the Higuchi ghost). For the cosmological constraints, we use data sets from the cosmic microwave background, baryon acoustic oscillations, and type Ia supernovae. Bimetric cosmology provides a good fit to data even for large values of the mixing angle between the massless and massive gravitons. Interestingly, the best-fit model is a self-accelerating solution where the accelerated expansion is due to the dynamical massive spin-2 field, without a cosmological constant. Due to the screening mechanism, the models are consistent with local tests of gravity such as solar system tests and gravitational lensing by galaxies. We also comment on the possibility of alleviating the Hubble tension with this theory.

Ghost-free bimetric gravity is an extension of general relativity, featuring a massive spin-2 field coupled to gravity. We parameterize the theory with a set of observables having specific physical interpretations. For the background cosmology and the static, spherically symmetric solutions (for example approximating the gravitational potential of the solar system), there are four directions in the parameter space in which general relativity is approached. Requiring that there is a working screening mechanism and a nonsingular evolution of the Universe, we place analytical constraints on the parameter space which rule out many of the models studied in the literature. Cosmological solutions where the accelerated expansion of the Universe is explained by the dynamical interaction of the massive spin-2 field rather than by a cosmological constant, are still viable.

Celebrating the centenary of general relativity theory, we must recall that Friedmann’s discovery of the equations of evolution of the Universe became the strongest prediction of this theory. These equations currently remain the foundation of modern cosmology. Nevertheless, data from new observations stimulate a search for modified theories of gravitation. We discuss cosmological aspects of theories with two dynamical metrics and theories of massive gravity, one of which was developed by Logunov and his coworkers.

It has been recently claimed [arXiv: 1510.00126], that the 143 GHz excess line in the Cosmic MicrowaveBackground (CMB) spectrumcould be explained by a collision of our Universe with an alternate Universe in which the baryon to entropy ratio is 65 times larger than the corresponding value measured for ourUniverse. This 143 GHz excess line is due to baryons, as was claimed, since the excess line corresponds to the recombination epoch, while the rest of the CMB signal is free of such excess lines. Thus the excess line is ascribed to an effect of collision of our Universe with a parallel universe. In this paper, we propose an alternative mechanism to explain the 143 GHz excess CMB line by using a simple bimetric gravity model which makes use of two metrics, the foreground metric g μν and the background metric f μν. The foreground Universe describes our Universe, and the background Universe is assumed to be underlying. The metrics are chosen to satisfy $${f_{\mu \nu }} = D_{{g_{\mu \nu }}}^2$$ , and the bimetric gravity model is constrained in such a way that the resulting Einstein equations for the background and foreground Universe are identical. In effect, the foreground and background Universe are indistinguishable at the cosmological solutions level. However, for the choices of the metrics we made, the scalar curvatures of the foreground and background Universes, namely R g and R f, are related by R f = 1/D 2, which can effectively result in different baryon to entropy ratios for the two Universes, via the gravitational baryogenesis mechanism. According to the gravitational baryogenesis mechanism, the baryon to entropy ratio is $$\eta B = \dot R/M_*^2T$$ , which means that the baryon to entropy ratio for the foreground and the background Universes we chose, namely ηB(g) and ηB(f), satisfy the relation $$\eta B\left( f \right) = \frac{1}{{{D^2}}}\eta B\left( g \right)$$ , and if D is chosen as $$D = 1/\sqrt {65} $$ , this could explain the 143 GHz excess line. The resulting phenomenological picture is quite appealing, since in the context of our bimetric gravity model, the foreground and background Universes coexist and are indistinguishable at the cosmological solutions level, but they are distinguishable only via the gravitational baryogenesis mechanism, which results in a baryon to entropy ratio for the background Universe, which is 65 time larger from the one corresponding to our Universe.

A notable feature of UV freeze-in is that the relic density is strongly dependent on the highest temperatures of the thermal bath, and a common assumption is that the relevant 'highest temperature' should be the reheating temperature after inflation $T_\text{RH}$. However, the temperature of the thermal bath can be significantly higher in certain scenarios, reaching a value denoted T max , a fact which is only apparent away from the instantaneous decay approximation. Interestingly, it has been shown that if the operators are of sufficiently high mass dimension then the dark matter abundance can be enhanced by a 'boost factor' depending on ($T_\text{max}/T_\text{RH}$) relative to naive estimates assuming instantaneous reheating. We highlight here that in non-standard cosmological histories the critical mass dimension of the operator above at which the instantaneous decay approximation breaks down, and the exponent of the boost factor, depend on the equation of state $\omega$ prior to reheating. We highlight four examples in which the dark matter abundance receives a significant enhancement in the context of gravitino dark matter, the moduli portal, the Higgs portal, and the spin-2 portal (as might arise in bimetric gravity models). We comment on the transition from kination domination to radiation domination as a motivated example of non-standard cosmologies., Comment: 22 pages, 5 figures

We propose an application of spectral geometry methods to the bimetric gravity models. The computation of the spectral action, using Wodzicki residua, may lead to the derivation of the effective action for this class of models. This is still work in progress.

We study spherically symmetric solutions in a four-parameter Einstein-Cartan-type class of theories. These theories include torsion, as well as the metric, as dynamical fields, and contain only two physical excitations (around flat spacetime): a massless spin-2 excitation and a massive spin-2 one (of mass $ m_2 \equiv \kappa$). They offer a geometric framework (which we propose to call "torsion bigravity") for a modification of Einstein's theory that has the same spectrum as bimetric gravity models. We find that the spherically symmetric solutions of torsion bigravity theories exhibit several remarkable features: (i) they have the same number of degrees of freedom as their analogs in ghost-free bimetric gravity theories ( i.e. one less than in ghost-full bimetric gravity theories); (ii) in the limit of small mass for the spin-2 field ($ \kappa \to 0$), no inverse powers of $\kappa$ arise at the first two orders of perturbation theory (contrary to what happens in bimetric gravity where $1/\kappa^2$ factors arise at linear order, and $1/\kappa^4$ ones at quadratic order). We numerically construct a high-compactness (asymptotically flat) star model in torsion bigravity and show that its geometrical and physical properties are significantly different from those of a general relativistic star having the same observable Keplerian mass., Comment: 28 pages, 3 figures

We discuss the connection between Weyl$^2$ supergravity and superstrings and further discuss holography between 4-dimensional, ${\cal N}=4$ superconformal Weyl$^2$ supergravity and ${\cal N}=8$, higher spin-four theory on $AdS_5$. The Weyl$^2$ plus Einstein supergravity theory is a special kind of a bimetric gravity theory and consists of a massless graviton multiplet plus an additional massive spin-two supermultiplet. Here, we argue that the additional spin-two field and its superpartners originate from massive excitations in the open string sector; just like the ${\cal N}=4$ super Yang-Mills gauge fields, they are localized on the world volume of D3-branes. The ghost structure of the Weyl action should be considered as an artifact of the truncation of the infinitely many higher derivative terms underlying the massive spin 2 action. In field theory, ${\cal N}=4$ Weyl$^2$ supergravity exhibits superconformal invariance in the limit of vanishing Planck mass. In string theory the additional spin-two fields become massless in the tensionless limit. Therefore low string scale scenarios with large extra dimensions provide (almost) superconformal field theories with almost massless open string spin-two fields. The full ${\cal N}=4$ scalar potential including the Yang-Mills matter multiplets is presented and the supersymmetric vacua of Einstein Supergravity are shown, as expected, to be vacua of massive Weyl supergravity. Other vacua are expected to exist which are not vacua of Einstein supergravity. Finally, we identify certain spin-four operators on the 4-dimensional boundary theory that could be the holographic duals of spin-four fields in the bulk., 33 pages, revised version with corrected typos and references added

The constraint algebra is derived in the second order tetrad Hamiltonian formalism of the bigravity. This is done by a straightforward calculation without involving any insights, implicit functions, and Dirac brackets. The tetrad approach is the only way to present the bigravity action as a linear functional of lapses and shifts and the Hassan–Rosen transform (characterized as ‘a complicated redefinition of the shift variable’ according to the authors) appears here not as an ansatz but as fixing of a Lagrange multiplier. A comparison of this approach with the other ones is provided.

Recently, Kenna-Allison et.al. claimed that bimetric gravity cannot give rise to a viable cosmological expansion history while at the same time being compatible with local gravity tests. In this note we review that claim and combine various results from the literature to provide several simple counter examples. We conclude that the results of Kenna-Allison et.al. cannot hold in general., 6 pages, 2 figures

We use the tetrad formalism to calculate a matrix square root occurring in the de Rham-Gabadadze-Tolley potential. In the minimal case, we obtain the constraints and their algebra. We show that the number of gravitational degrees of freedom corresponds to the massless and massive gravity fields. The Boulware-Deser ghost is eliminated because of two second-class constraints.

Recent re-calibration of the Type Ia supernova (SNe~Ia) magnitude-redshift relation combined with cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) data have provided excellent constraints on the standard cosmological model. Here, we examine particular classes of alternative cosmologies, motivated by various physical mechanisms, e.g. scalar fields, modified gravity and phase transitions to test their consistency with observations of SNe~Ia and the ratio of the angular diameter distances from the CMB and BAO. Using a model selection criterion for a relative comparison of the models (the Bayes Factor), we find moderate to strong evidence that the data prefer flat $\Lambda$ CDM over models invoking a thawing behaviour of the quintessence scalar field. However, some exotic models like the growing neutrino mass cosmology and vacuum metamorphosis still present acceptable evidence values. The bimetric gravity model with only the linear interaction term can be ruled out by the combination of SNe~Ia and CMB/BAO datasets whereas the model with linear and quadratic interaction terms has a comparable evidence value to standard $\Lambda$ CDM. Thawing models are found to have significantly poorer evidence compared to flat $\Lambda$ CDM cosmology under the assumption that the CMB compressed likelihood provides an adequate description for these non-standard cosmologies. We also present estimates for constraints from future data and find that geometric probes from oncoming surveys can put severe limits on non-standard cosmological models., Comment: 31 pages, 9 figures, to be submitted to JCAP. Comments welcome

We consider the parametrized post-Newtonian (PPN) limit of ghost-free massive bimetric gravity with two mutually non-interacting matter sectors coupled to the two metrics. Making use of a gauge-invariant differential decomposition of the metric perturbations, we solve the field equations up to the linear PPN order for a static, point-like mass source. From the result we derive the PPN parameter $\gamma$ for spherically symmetric systems, which describes the gravitational deflection of light by visible matter. By a comparison to its value measured in the solar system we obtain bounds on the parameters of the theory. We further discuss the deflection of light by dark matter and find an agreement with the observed light deflection by galaxies. We finally speculate about a possible explanation for the observed distribution of dark matter in galactic mergers such as Abell 520 and Abell 3827., Comment: 36 pages, 1 figure; journal version

We describe the freedom of choosing a square root in massive gravity from algebraic point of view. This contribution is based on the talk given by one of us (AG) at the Geometric Foundations of Gravity conference in Tartu in August 2017., Comment: 9 pages, 1 figure; some typos corrected

The bimetric generalization of general relativity has been proven to be able to give an accelerated background expansion consistent with observations. Apart from the energy densities coupling to one or both of the metrics, the expansion will depend on the cosmological constant contribution to each of them, as well as the three parameters describing the interaction between the two metrics. Even for fixed values of these parameters can several possible solutions, so called branches, exist. Different branches can give similar background expansion histories for the observable metric, but may have different properties regarding, for example, the existence of ghosts and the rate of structure growth. In this paper, we outline a method to find viable solution branches for arbitrary parameter values. We show how possible expansion histories in bimetric gravity can be inferred qualitatively, by picturing the ratio of the scale factors of the two metrics as the spatial coordinate of a particle rolling along a frictionless track., Comment: 17 pages, 4 figures. Matches version published in JCAP

In many generalized models of gravity, perfect fluids in cosmology give rise to gravitational slip. Simultaneously, in very broad classes of such models, the propagation of gravitational waves is altered. We investigate the extent to which there is a one-to-one relationship between these two properties in three classes of models with one extra degree of freedom: scalar (Horndeski and beyond), vector (Einstein-Aether) and tensor (bimetric). We prove that in bimetric gravity and Einstein-Aether, it is impossible to dynamically hide the gravitational slip on all scales whenever the propagation of gravitational waves is modified. Horndeski models are much more flexible, but it is nonetheless only possible to hide gravitational slip dynamically when the action for perturbations is tuned to evolve in time toward a divergent kinetic term. These results provide an explicit, theoretical argument for the interpretation of future observations if they disfavoured the presence of gravitational slip., 14 pages; v2 reflects that accepted for publication in PRD. Discussion of proof for Horndeski significantly improved