We construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint fields. We perform explicit conformal transformations to demonstrate the physical equivalence between the Jordan and Einstein frames at the level of quadratic perturbations. We show how to generalize the formalism to the case of a more complicated scalar sector with an internal symmetry, such as Higgs inflation. This work represents a first step in developing gauge invariant perturbation theory for nonminimally coupled inflationary models.
We investigate preheating of an inflaton field $ϕ$ coupled nonminimally to a spacetime curvature. In the case of a self-coupling inflaton potential $V(ϕ)=λϕ^4/4$, the dynamics of preheating changes by the effect of the negative $ξ$. We find that the nonminimal coupling works in two ways. First, since the initial value of inflaton field for reheating becomes smaller with the increase of $|ξ|$, the evolution of the inflaton quanta is delayed for fixed $λ$. Second, the oscillation of the inflaton field is modified and the nonadiabatic change around $ϕ=0$ occurs significantly. That makes the reson…
Nonminimally coupled inflation models based on a nonminimal coupling $ξϕ^{2} R$ and a $ϕ^{4}$ potential are in excellent agreement with the scalar spectral index observed by Planck. Here we consider the modification of these models by a conformal factor with a zero. This enables a nonminimally coupled model to have a Planck-scale potential energy density at large values of the inflaton field, which can account for the smooth, potential-dominated volume that is necessary for inflation to start. We show that models with a conformal factor zero generally predict a correlated increase of the spect…
We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models, and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill-defined at the quantum level in the high energy/sub horizon regime (…
In this paper we show that the on-shell Lagrangian of a perfect fluid depends on microscopic properties of the fluid, giving specific examples of perfect fluids with different on-shell Lagrangians but with the same energy-momentum tensor. We demonstrate that if the fluid is constituted by localized concentrations of energy with fixed rest mass and structure (solitons) then the average on-shell Lagrangian of a perfect fluid is given by ${\mathcal L}_m=T$, where $T$ is the trace of the energy-momentum tensor. We show that our results have profound implications for theories of gravity where the m…
The nonminimal coupling of the kinetic term to Einstein's tensor helps the implementation of inflationary models due to the gravitationally enhanced friction. We calculate the parametrized post-Newtonian (PPN) parameters for the scalar--tensor theory of gravity with nonminimally derivative coupling. We find that under experimental constraint from the orbits of millisecond pulsars in our galaxy, the theory deviates from Einstein's general relativity in the order of $10^{-20}$, and the effect of the nonminimal coupling is negligible if we take the scalar field as dynamical dark energy. With the …
We present a cosmological model arising from a gravitational theory with an infinite tower of higher-order curvature invariants that can reproduce the entire evolution of the Universe: from inflation to late-time acceleration, without invoking an inflaton nor a cosmological constant. The theory is Einsteinian-like. The field equations for a Friedmann-Lemaître-Robertson-Walker metric are of second-order and can reproduce a late-time evolution that is consistent with the acceleration provided by the cosmological constant at low redshift. Our results force us to reinterpret the nature of dark ene…
We show that the inflaton coupling to all other fields is exponentially suppressed during inflation in the cosmological $α$-attractor models. In the context of supergravity, this feature is a consequence of the underlying hyperbolic geometry of the moduli space which has a flat direction corresponding to the inflaton field. A combination of these factors protects the asymptotic flatness of the inflaton potential.
We investigate the backreaction of the quantum fluctuations of a very light ($m \!\lesssim\! H_{\text{today}}$) nonminimally coupled spectator scalar field on the expansion dynamics of the Universe. The one-loop expectation value of the energy momentum tensor of these fluctuations, as a measure of the backreaction, is computed throughout the expansion history from the early inflationary universe until the onset of recent acceleration today. We show that, when the nonminimal coupling $ξ$ to Ricci curvature is negative ($ξ_c \!=\! 1/6$ corresponding to conformal coupling), the quantum backreacti…
We present the first symmetry inheritance analysis of fields nonminimally coupled to gravity. In this work we are focused on the real scalar field $ϕ$ with nonminimal coupling of the form $ξϕ^2 R$. Possible cases of the symmetry noninheriting fields are constrained by the properties of the Ricci tensor and the scalar potential. Examples of such spacetimes can be found among those which are "dressed" with the stealth scalar field, a nontrivial scalar field configuration with the vanishing energy-momentum tensor. We classify the scalar field potentials which allow the symmetry noninheriting stea…
We explore dynamics of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models including the Hilbert-Einstein curvature term and the $N$ degree monomial of the scalar field nonminimally coupled to gravity. The potential of the scalar field is the $n$ degree monomial or polynomial. We describe several qualitatively different types of dynamics depending on values of power indices $N$ and $n$. We identify that three main possible pictures correspond to $n<N$, $N<n<2N$ and $n>2N$ cases…
We study slow-roll inflation with a Gauss-Bonnet term that is coupled to an inflaton field nonminimally. We investigate the inflationary solutions for a specific type of the nonminimal coupling to the Gauss-Bonnet term and inflaton potential both analytically and numerically. We also calculate the observable quantities such as the power spectra of the scalar and tensor modes, the spectral indices, the tensor-to-scalar ratio and the running spectral indices. Finally, we constrain our result with the observational data by Planck and BICEP2 experiment.
Recently, it has been shown that during preheating the entropy modes circulating in the loops, which correspond to the inflaton decay products, meaningfully modify the cosmological correlation functions at superhorizon scales. In this paper, we determine the significance of the same effect when reheating occurs in the perturbative regime. In a typical two scalar field model, the magnitude of the loop corrections are shown to depend on several parameters like the background inflaton amplitude in the beginning of reheating, the inflaton decay rate and the inflaton mass. Although the loop contrib…
We study the Vainshtein screening mechanism in Horndeski theories in the presence of a scalar field $ϕ$ nonminimally and kinetically coupled to ordinary matter field. A general interacting Lagrangian describing this coupling is characterized by energy transfer $f_1$ and momentum exchange $f_2$. For a spherically symmetric configurations on top of the cosmological background, we investigate the static perturbations in linear and nonlinear regimes with respect to the scalar field perturbation. In the former regime, the parametrized post-Newtonian parameter generally deviates from unity as long a…
A special class of conformal gravity theories is proposed to solve the long standing problem of the fine-tuned cosmological constant. In the proposed model time evolution of the inflaton field leaves behind a nearly vanishing, but finite value of dark energy density of order (a few meV)$^4$ to explain the late-time accelerating universe. A multiple scalar inflaton field is assumed to have a conformal coupling to the Ricci scalar curvature in the lagrantian, which results in, after a Weyl rescaling to the Einstein metric frame, modification of inflaton kinetic and potential terms along with its…
We extend the concept of quintessence to a flat nonminimally coupled scalar - tensor theories of gravity. By means of Noether's symmetries for the cosmological pointlike Lagrangian L, it is possible to exhibit exact solutions for a class of models depending on a free parameter s. This parameter comes out in the relationship existing between the coupling F(ϕ) and the potential V(ϕ) because of such a symmetry for L. When inverse power law potentials are taken in account, a whole family of exact solutions parametrized by such an s is proposed as a class of tracker fields, and some considerations …
We show that, by adding a gauge singlet scalar S to the standard model which is nonminimally coupled to gravity, S can act both as the inflaton and as thermal relic dark matter. We obtain the allowed region of the (m_s, m_h) parameter space which gives a spectral index in agreement with observational bounds and also produces the observed dark matter density while not violating vacuum stability or nonperturbativity constraints. We show that, in contrast to the case of Higgs inflation, once quantum corrections are included the spectral index is significantly larger than the classical value (n = …
Recently, few cosmological models with additional non-Riemannian volume form(s) have been proposed. In this article we use Supernovae type Ia experimental data to test one of these models which provides a unified description of both dark energy via dynamically generated cosmological constant and dark matter as a "dust" fluid due to a hidden nonlinear Noether symmetry. It turns out that the model allows various scenarios of the future Universe evolution and in the same time perfectly fits contemporary observational data. Further, we investigate the influence of an additional inflaton field with…
The Starobinsky model, considered in the framework of the Palatini formalism, in contrast to the metric formulation, does not provide us with a model for inflation, due to the absence of a propagating scalar degree of freedom that can play the role of the inflaton. In the present article we study the Palatini formulation of the Starobinsky model coupled, in general nonminimally, to scalar fields and analyze its inflationary behavior. We consider scalars, minimally or nonminimally coupled to the Starobinsky model, such as a quadratic model, the induced gravity model or the standard Higgs-like i…
In the path integral formulation of the reduced phase space Loop Quantum Gravity (LQG), we propose a new approach to allow the spatial cubic lattice (graph) to change dynamically in the physical time evolution. The equations of motion of the path integral derive the effective dynamics of cosmology from the full LQG, when we focus on solutions with homogeneous and isotropic symmetry. The resulting cosmological effective dynamics with the dynamical lattice improves the effective dynamics obtained earlier from the path integral with fixed spatial lattice: The improved effective dynamics recovers …
Cosmological models with an SU(2) Yang-Mills field are studied. For a specific model with a minimally coupled Yang-Mills Lagrangian, which includes an arbitrary function of the second-order term and a fourth-order term, a corresponding reconstruction program is proposed. It is shown that the model with minimal coupling has no de Sitter solutions, for any nontrivial function of the second-order term. To get de Sitter solutions, a gravitational model with nonminimally coupled Yang-Mills fields is then investigated. It is shown that the model with non-minimal coupling has in fact a de Sitter solu…
The $N=1$ supergravity models of cosmological inflation with inflaton belonging to a massive vector multiplet and spontaneous SUSY breaking after inflation are reformulated as the supersymmetric $U(1)$ gauge theories of a massless vector superfield interacting with the Higgs and Polonyi chiral superfields, all coupled to supergravity. The $U(1)$ gauge sector is identified with the $U(1)$ gauge fields of the super-GUT coupled to supergravity, whose gauge group has a $U(1)$ factor. A positive cosmological constant (dark energy) is included. The scalar potential is calculated, and its de Sitter v…
In a recent work, we demonstrated that a modified gravity model in which a scalar "darkon" field is coupled to both the standard Riemannian metric and to another non-Riemannian volume form is compatible with observational data from Supernovae Type Ia. Here, we investigate a more complicated model with an additional "inflaton" scalar field. We demonstrate numerically that the model can qualitatively reproduce the Universe inflation epoch, matter dominated epoch, and present accelerating expansion in a seamless way. We show that such solutions occur only when the model parameters are within a ve…
The cosmological constant (term) is the simplest way, presently known, to illustrate the accelerating expansion of the universe. However, because of/despite its simple appearance, there is much confusion surrounding its essence. Theorists have been asking questions for years: Is there a mechanism to explain this term? Is it really a constant or a variable? Moreover, it seems that we have created a huge gulf separating the theories of inflation and accelerating expansion. Can we eliminate such an uncomfortable discontinuity? Abstract In this paper, we will journey to see the growth of the unive…
We investigate multi-field signatures of the nonminimally coupled supersymmetric Higgs inflation-type cosmological scenario, focusing on the two-field Higgs-lepton inflation model as a concrete example. This type of inflationary model is realized in a theory beyond the Standard Model embedded in supergravity with a noncanonical Kähler potential. We employ the backward $δN$ formalism to compute cosmological observables, including the scalar and tensor power spectra, the spectral indices, the tensor-to-scalar ratio and the local-type nonlinearity parameter. The trajectory of the inflaton is cont…
In dark energy models where a scalar field $ϕ$ is coupled to the Ricci scalar $R$ of the form $e^{-2Q (ϕ-ϕ_0)/M_{\rm pl}}R$, where $Q$ is a coupling constant, $ϕ_0$ is today's value of $ϕ$, and $M_{\rm pl}$ is the reduced Planck mass, we study how the recent Lunar Laser Ranging (LLR) experiment places constraints on the nonminimal coupling from the time variation of gravitational coupling. Besides a potential of the light scalar responsible for cosmic acceleration, we take a cubic Galileon term into account to suppress fifth forces in over-density regions of the Universe. Even if the scalar-ma…
We investigate scalar perturbations from inflation in a bulk inflaton braneworld model. Using the generalized longitudinal gauge, we derive and solve the full set of scalar perturbation equations. Our exact results support the recent argument that for the de Sitter brane the square of the radion mass is not positive, showing that unlike the flat brane case, the de Sitter brane is not stable.
We explore the cosmological consequences of having the fluctuations of the inflaton field entangled with those of another scalar, within the context of a toy model consisting of non-interacting, minimally coupled scalars in a fixed de Sitter background. We find that despite the lack of interactions in the Lagrangian, the initial state entanglement modifies the mode equation for the inflaton fluctuations and thus can induce changes in cosmological observables. These effects are examined for a variety of choices of masses and we find that they can be consistent with the requirement that the back…
We have carried out detailed $k$-mode analysis of single-inflaton slow-roll inflationary perturbations including quantum fluctuations by setting up non-linear coupled differential equations of inflaton field ($ϕ$), its perturbation ($δϕ$) and the metric perturbation (the Bardeen potential, $Φ_B$), and calculated the number of e-folds ($N$), scalar spectral index ($n_s$), tensor spectral index ($n_h$), scalar power spectrum ($Δ_s$), tensor power spectrum ($Δ_h$), tensor-to-scalar ratio ($r$) and the Hubble parameter ($H$) for different $k$ values at the horizon crossing. In these calculations w…
In construction of an inflationary model, one usually assumes that the matter sector of the gravitational action is minimally coupled to the background. It means that the matter (inflaton) part of the action is coupled with the same metric of the gravitational part. We elaborate on this assumption and investigate some of the consequences. We assume that the gravitational and the inflaton sectors belong to different units (or conformal frames). We show that this coupling can convert a single-field inflationary model into a two-field one with a mixed kinetic term. The energy-momentum tensor of t…
Cosmological inflation is studied in the case where the inflaton is the overall modulus $T$ for an orbifold. General forms of the (non-perturbative) superpotential are considered to ensure that $G=K+{\rm ln}|W|^2$ is modular invariant. We find generically that these models do not produce a potential flat enough for slow roll to a supersymmetric minimum, although we do find a model which produces up to 20 e-folds of inflation to a non-supersymmetric minimum.
We study quantum fluctuations of a free massless scalar field during inflation in the presence of a point, line, or plane defect such as a black hole, cosmic string, or domain wall, using a perturbative expansion in powers of small defect parameters. We provide results for the scalar two-point correlation functions that show explicitly a small violation of translational invariance during inflation.
We propose a new mechanism of lepton (L) number asymmetry generation, hence offer an explanation of matter-antimatter imbalance when a significant amount of baryon number is later transformed from this L-number by known electroweak sphaleron mediated process. The basic theoretical framework is a recently proposed multiple scalar-tensor gravity that dynamically solves the cosmological constant problem. The L-asymmetry generation in one of two proposed scenarios is triggered by dynamical relaxation of scalar inflaton field towards the zero cosmological constant. CPT violation (C= charge conjugat…
We apply a recently developed 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation for the study of spherically symmetric, static black hole solutions of Horndeski scalar-tensor theory. Our discussion proceeds in an effective field theory (EFT) of modified gravity approach, with the action depending on metric and embedding scalars adapted to the nonorthogonal 2+1+1 decomposition. We prove that the most generic class of Horndeski Lagrangians compatible with observations can be expressed in this EFT form. By studying the first order perturbation of the EFT action we derive…
Inflationary $α$-attractor models in supergravity, which provide excellent fits to the latest observational data, are based on the Poincare disk hyperbolic geometry. We refine these models by constructing Kahler potentials with built-in inflaton shift symmetry and by making a canonical choice of the goldstino Kahler potential. The refined models are stable with respect to all scalar fields at all $α$, no additional stabilization terms are required. The scalar potential V has a nearly Minkowski minimum at small values of the inflaton field $φ$, and an infinitely long dS valley of constant depth…
We consider power-law inflation with a Gauss-Bonnet correction inspired by string theory. We analyze the stability of cosmological perturbations and obtain the allowed parameter space. We find that for GB-dominated inflation ultra-violet instabilities of either scalar or tensor perturbations show up on small scales. The Gauss-Bonnet correction with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio in the potential-dominated case. We place tight constraints on the model parameters by making use of the WMAP 5-year data.
If the cosmological inflationary scenario took place in the cosmic landscape in string theory, the inflaton, the scalar mode responsible for inflation, would have meandered in a complicated multi-dimensional potential. We show that this meandering property naturally leads to many e-folds of inflation, a necessary condition for a successful inflationary scenario. This behavior also leads to fluctuations in the primordial power spectrum of the cosmic microwave background radiation, which may be detected in a near future cosmic variance limited experiment like PLANCK.
We suggest a path integral formulation for the tunneling cosmological state, which admits a consistent renormalization and renormalization group (RG) improvement in particle physics applications of quantum cosmology. We apply this formulation to the inflationary cosmology driven by the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. In this way a complete cosmological scenario is obtained, which embraces the formation of initial conditions for the inflationary background in the form of a sharp probability peak in the distribution o…
We study an effective 4-dimensional scalar-tensor field theory, originated from an underlying brane-bulk warped geometry, to explore the scenario of inflation. It is shown that the inflaton potential naturally emerges from the radion energy-momentum tensor which in turn results into an inflationary model of the Universe on the visible brane that is consistent with the recent results from the Planck's experiment. The dynamics of modulus stabilization from the inflaton rolling condition is demonstrated. The implications of our results in the context of recent BICEP2 results are also discussed.
We propose a qualitatively new mechanism for generating cosmological fluctuations from inflation. The non-equilibrium excitation of interacting scalar fields often evolves into infra-red (IR) and ultra-violet (UV) cascading, resulting in an intermediate scaling regime. We observe elements of this phenomenon in a simple model with inflaton ϕand iso-inflaton χfields interacting during inflation via the coupling g^2 (ϕ-ϕ_0)^2 χ^2. Iso-inflaton particles are created during inflation when they become instantaneously massless at ϕ=ϕ_0, with occupation numbers not exceeding unity. We point out that v…
Alternative theories of gravity and their solutions are of considerable importance since at some fundamental level the world can reveal new features. Indeed, it is suspected that the gravitational field might be nonminimally coupled to the other fields at scales not yet probed, bringing into the forefront nonminimally coupled theories. In this mode, we consider a nonminimal Einstein-Yang-Mills theory with a cosmological constant. Imposing spherical symmetry and staticity for the spacetime and a magnetic Wu-Yang ansatz for the Yang-Mills field, we find expressions for the solutions of the theor…
Adiabatic (curvature) perturbations are produced during a period of cosmological inflation that is driven by a single scalar field, the inflaton. On particle physics grounds -- though -- it is natural to expect that this scalar field is coupled to other scalar degrees of freedom. This gives rise to oscillations between the perturbation of the inflaton field and the perturbations of the other scalar degrees of freedom, similar to the phenomenon of neutrino oscillations. Since the degree of the mixing is governed by the squared mass matrix of the scalar fields, the oscillations can occur even if…
Cosmological alpha-attractors give a natural explanation for the spectral index n_s of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future detection of gravity waves. Their embedding into supergravity exploits the hyperbolic geometry of the Poincare disk or half-plane. These geometries are isometric under Mobius transformations, which include the shift symmetry of the inflaton field. We introduce a new Kahler potential frame that explicitly preserves this symmetry, enabling the infl…
We propose a new way to implement an inflationary prior to a cosmological dataset that incorporates the inflationary observables at arbitrary order. This approach employs an exponential form for the Hubble parameter $H(ϕ)$ without taking the slow-roll approximation. At lowest non-trivial order, this $H(ϕ)$ has the unique property that it is the solution to the brachistochrone problem for inflation.
A simple model for the reheating of the universe after inflation is studied in which an essentially inhomogeneous scalar field representing matter is coupled to an essentially homogeneous scalar inflaton field. Through this coupling, the potential determining the evolution of the inflaton field is made time-dependent. Due to this the frequency of parametric resonance becomes time dependent, making the reheating process especially effective. All fields including the gravitational field are initially simplified by expanding each in terms of the respective homogeneity or inhomogeneity. Employing …
We investigate cosmology with complex scalar field. It is shown that such models can describe two stages of inflation and the oscillatory regime. Thus we don't need both quintessence and $Λ$-term. It is enough to have single complex field to obtain both inflation and present accelerated universe. If the present accelerated expansion was created by the complex field then universe must escape eternal acceleration. Besides, we will show that cosmological equations with complex field admit stationary solution without any cosmological constant.
We study the scalar sector of the Two Measures Field Theory (TMT) model in the context of cosmological dynamics. The scalar sector includes the inflaton ϕand the Higgs \upsilon fields. The model possesses gauge and scale invariance. The latter is spontaneously broken due to intrinsic features of the TMT dynamics. In the model with the inflaton ϕalone, in different regions of the parameter space the following different effects can take place without fine tuning of the parameters and initial conditions: a) Possibility of resolution of the old cosmological constant problem: this is done in a cons…
Decay of the inflaton or moduli which dominated the energy density of the universe at early times leads to a matter to radiation transition epoch. We consider non-thermal sterile dark matter particles produced as decay product during such transitions. The particles have a characteristic energy distribution - that associated with decays taking place in a matter dominated universe evolving to radiation domination. We primarily focus on the case when the particles are hot dark matter, and study their effects on the Cosmic Microwave Background (CMB) and Large Scale Structure (LSS), explicitly taki…
We describe a broad class of multi-field inflationary models with spontaneously broken conformal invariance. It generalizes the recently discovered class of cosmological attractors with a single inflaton field. In the new multi-field theories, just as in the previously studied single-field models, the moduli space has a boundary (Kahler cone) in terms of the original homogeneous conformal variables. Upon spontaneous breaking of the conformal invariance and switching to the Einstein frame, this boundary moves to infinity in terms of the canonically normalized inflaton field. This results in the…
The density perturbations generated when the inflaton decay rate is perturbed by a light scalar field $χ$ are studied. By explicitly solving the perturbation equations for the system of two scalar fields and radiation, we show that even in low energy-scale inflation nearly scale-invariant spectra of scalar perturbations with an amplitude set by observations are obtained through the conversion of $χ$ fluctuations into adiabatic density perturbations. We demonstrate that the spectra depend on the average decay rate of the inflaton & on the inflaton fluctuations. We then apply this new mechanism …
We study the role of the Standard Model Higgs condensate, formed during cosmological inflation, in the epoch of reheating that follows. We focus on the scenario where the inflaton decays slowly and perturbatively, so that there is a long period between the end of inflation and the beginning of radiation domination. The Higgs condensate decays non-perturbatively during this period, and we show that it heats the primordial plasma to much higher temperatures than would result from the slowly-decaying inflaton alone. We discuss the effect of this hot plasma on the thermalization of the inflaton's …
We suggest a new type of hill-top inflation originating from the initial conditions in the form of the microcanonical density matrix for the cosmological model with a large number of quantum fields conformally coupled to gravity. Initial conditions for inflation are set up by cosmological instantons describing underbarrier oscillations in the vicinity of the inflaton potential maximum. These periodic oscillations of the inflaton field and cosmological scale factor are obtained within the approximation of two coupled oscillators subject to the slow roll regime in the Euclidean time. This regime…
The quantum fluctuations of the Higgs field during inflation could be a source of primordial density perturbations through Higgs-dependent inflaton decay. By measuring primordial non-Gaussianities, this so-called Higgs-modulated reheating scenario provides us a unique chance to probe Higgs interactions at extremely high energy scale, which we call the Cosmological Higgs Collider (CHC). We realize CHC in a simple scenario where the inflaton decays into Higgs-portal scalars, taking account of the decay of the Higgs fluctuation amplitude after inflation. We also calculate the CHC signals of Stand…
