We investigate the consequences of non-minimal gravitational coupling to matter and study how it differs from the case of minimal coupling by choosing certain simple forms for the nature of coupling, The values of the parameters are specified at $z=0$ (present epoch) and the equations are evolved backwards to calculate the evolution of cosmological parameters. We find that the Hubble parameter evolves more slowly in non-minimal coupling case as compared to the minimal coupling case. In both the cases, the universe accelerates around present time, and enters the decelerating regime in the past. Using the latest Union2 dataset for supernova Type Ia observations as well as the data for baryon acoustic oscillation (BAO) from SDSS observations, we constraint the parameters of Linder exponential model in the two different approaches. We find that there is a upper bound on model parameter in minimal coupling. But for non-minimal coupling case, there is range of allowed values for the model parameter.
A non-minimally coupled scalar field can have, in principle, a negative effective Planck mass squared which depends on the scalar field. Surprisingly, an isotropic and homogeneous cosmological universe with a non-minimally coupled scalar field is perfectly smooth as the rolling scalar field causes the effective Planck mass to change sign and pass through zero. However, we show that any small deviations from homogeneity diverge as the effective Planck mass vanishes, with catastrophic consequences for the cosmology. The physical origin of the divergence is due to the presence of non-zero scalar …
We calculate the quantum gravitational corrections to the Mukhanov-Sasaki equation obtained by the canonical quantization of the inflaton-gravity system. Our approach, which is based on the Born-Oppenheimer decomposition of the resulting Wheeler-DeWitt equation, was previously applied to a minimally coupled inflaton. In this article we examine the case of a non minimally coupled inflaton and, in particular, the induced gravity case is also discussed. Finally, the equation governing the quantum evolution of the inflationary perturbations is derived on a de Sitter background. Moreover the proble…
We consider the renormalization group improvement in the theory of the Standard Model Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. It suggests the range of the Higgs mass $135.6 {\rm GeV} \lesssim M_H\lesssim 184.5 {\rm GeV}$ compatible with the current CMB data (the lower WMAP bound on $n_s$), which is close to the widely accepted range dictated by the electroweak vacuum stability and perturbation theory bounds. We find the phenomenon of asymptotic freedom induced by this non-minimal curvature coupling, which brings the theory to the weak coupling…
Conformally related metrics and Lagrangians are considered in the context of scalar-tensor gravity cosmology. After the discussion of the problem, we pose a lemma in which we show that the field equations of two conformally related Lagrangians are also conformally related if and only if the corresponding Hamiltonian vanishes. Then we prove that to every non-minimally coupled scalar field, we may associate a unique minimally coupled scalar field in a conformally related space with an appropriate potential. The latter result implies that the field equations of a non-minimally coupled scalar fiel…
In this publication we investigate dynamics of a flat FRW cosmological model with a non-minimally coupled scalar field with the coupling term $ξR ψ^{2}$ in the scalar field action. The quadratic potential function $V(ψ)\propto ψ^{2}$ is assumed. All the evolutional paths are visualized and classified in the phase plane, at which the parameter of non-minimal coupling $ξ$ plays the role of a control parameter. The fragility of global dynamics with respect to changes of the coupling constant is studied in details. We find that the future big rip singularity appearing in the phantom scalar field c…
This thesis presents research exploring aspects of inflation and cosmology in the context of inflation models in which an inflaton is non-minimally coupled to the Ricci scalar, or is considered in conjunction with a term quadratic in the Ricci scalar. We consider a $ϕ^{2}$ Palatini inflation model in $R^{2}$ gravity and investigate whether this model can overcome some of the problems of the original $ϕ^{2}$ chaotic inflation model. We investigate the compatibility of this model with the observed CMB when treated as an effective theory of inflation in quantum gravity by examining the constraint…
Cosmology with a Non-minimally Coupled Dark Matter Fluid I. Background Evolution
SISSA（斯issa国际高等研究学院）；Institute for Fundamental Physics of the Universe (IFPU)（宇宙基础物理研究所）；INFN-Sezione di Trieste（的里雅斯特意大利国家核物理研究所）；IRA-INAF（博洛尼亚天文台研究所）
We argue that double inflation may occur when a spectator field is non-minimally coupled to gravity. As a concrete example, we study a two-field inflationary model where the initial spectator field is non-minimally coupled to gravity while the initial inflaton field is minimally coupled. The non-minimal coupling results in the growth of the spectator field which, in turn, drives the second stage of inflation in a significant region of parameter space. The isocurvature fluctuations originating from the spectator field source adiabatic ones, and hence the spectator non-minimal coupling can modif…
We study integrable models in the Bianchi I metric case with scalar fields minimally and non-minimally coupled with gravity and the correspondence between their general solutions. Using the model with a minimally coupled scalar field and a constant potential as an example, we demonstrate how to obtain the general solutions of the corresponding models in the Jordan frame.
In this paper, we consider rolling tachyon, with steep run-away type of potentials non-minimally coupled to massive neutrino matter. The coupling dynamically builds up at late times as neutrino matter turns non-relativistic. In case of scaling and string inspired potentials, we have shown that non-minimal coupling leads to minimum in the field potential. Given a suitable choice of model parameters, it is shown to give rise to late-time acceleration with the desired equation of state.
We consider generic models of quintessence and we investigate the influence of massive neutrino matter with field-dependent masses on the matter power spectrum. In case of minimally coupled neutrino matter, we examine the effect in tracker models with inverse power-law and double exponential potentials. We present detailed investigations for the scaling field with a steep exponential potential, non-minimally coupled to massive neutrino matter, and we derive constraints on field-dependent neutrino masses from the observational data.
We compute the greybody factors for non-minimally coupled scalar fields in four-dimensional Schwarzschild-de Sitter spacetime. In particular, we demonstrate that the zero-angular-momentum greybody factor generically tends to zero in the zero-frequency limit like frequency squared if there is non-vanishing coupling to the scalar curvature. This is in contrast with the minimally coupled case, where the greybody factor is known to tend to a finite constant. We also study the Hawking radiation for non-minimally coupled massless scalar fields in Schwarzschild-de Sitter spacetime, formulate a sensib…
We demonstrate the existence of Q-balls in non-minimally coupled inflation models with a complex inflaton in the Palatini formulation of gravity. We show that there exist Q-ball solutions which are compatible with inflation and we derive a window in the inflaton mass squared for which this is the case. In particular, we confirm the existence of Q-ball solutions with $ϕ\sim 10^{17}-10^{18}$ GeV, consistent with the range of field values following the end of slow-roll Palatini inflation. We study the Q-balls and their properties both numerically and in an analytical approximation. The existence …
We obtain traversable wormhole and time machine solutions of the field equations of an alternative of gravity with non-minimally curvature-matter coupling. Our solutions exhibit a non-trivial redshift function and allow for matter that satisfy the dominant energy condition.
We study evolution of cosmological models filled with the scalar field and barotropic matter. We consider the scalar field minimally and non-minimally coupled to gravity. We demonstrated the growth of degree of complexity of evolutional scenario through the description of matter content in terms of the scalar field. In study of all evolutional paths for all initial conditions methods of dynamical systems are used. Using linearized solutions we present simple method of derivation corresponding form of the Hubble function of the scale factor $H(a)$.
We study the cosmological evolution and singularity crossing in the Bianchi-I universe filled with a conformally coupled scalar field and compare them with those of the Bianchi-I universe filled with a minimally coupled scalar field. We also write down the solution for the Bianchi-I Universe in the induced gravity cosmology.
We study the minimally and non-minimally coupled scalar field models as possible alternatives for dark energy, the mysterious energy component that is driving the accelerated expansion of the universe. After discussing the dynamics at both the background and perturbation level, we confront the two models with the latest cosmological data. After obtaining updated constraints on their parameters we perform model selection using the basic information criteria. We found that the $Λ$CDM model is strongly favored when the local determination of the Hubble constant is not considered and that this sta…
Dynamical systems methods are used to study the evolution of the Bianchi I model with a scalar field. We show that inclusion of the non-minimal coupling term between the scalar field and the curvature changes evolution of the model compared with the minimally coupled case. In the model with the non-minimally coupled scalar field there is a new type of singularity dominated by the non-minimal coupling term. We examine the impact of the non-minimal coupling on the anisotropy evolution and demonstrate the existence of its minimal value in the generic case.
We, in the first part, contemplate a massless minimally coupled scalar which is Yukawa-coupled to a massless Dirac fermion in a locally de Sitter background of an inflating spacetime. We compute the scalar's quantum corrected mode function, power spectrum, spectral index and the running of the spectral index at one-loop order. We find that the spectrum is slightly blue-tilted; hence, the amplitudes of fluctuations grow slightly toward the smaller scales. Then, in the second part, we apply the computation method used in the first part to a massless minimally coupled scalar with a quartic self-i…
We study the inflation in a model with a Gauss-Bonnet term which is non-minimally coupled to a DBI field. We study the spectrum of the primordial perturbations in detail. The non-Gaussianity of this model is considered and the amplitude of the non-Gaussianity is studied in both the equilateral and orthogonal configurations. By taking various functions of the DBI field, inflaton potential and the Gauss-Bonnet coupling term, we test the model with observational data and find some constraints on the Gauss-Bonnet coupling parameter.
Scalar-tensor Cosmologies can be dealt under the standard of the Hojman conservation theorem that allows to fix the form of the coupling $F(ϕ)$, of the potential $V(ϕ)$ and to find out exact solutions for related cosmological models. Specifically, the existence of a symmetry transformation vector for the equations of motion gives rise to a Hojman conserved quantity on the corresponding minisuperpace and exact solutions for the cosmic scale factor $a$ and the scalar field $ϕ$ can be achieved. In particular, we take advantage of the fact that minimally coupled solutions, previously obtained in t…
We investigate some cosmological models arising from a non-minimal coupling of a fermionic field to gravity in the geometrical setting of Einstein-Cartan-Sciama-Kibble gravity. The role played by the non-minimal coupling together with torsion in facing problems such as cosmological singularity, inflation and dark energy is discussed.
Properties of soliton stars that could be expected to naturally arise out of a first order phase transition in non-minimally coupled scalar-field-induced gravity theories are investigated. Of particular interest are configurations, similar to Lee-Wick stars, with vanishing effective gravitational constant in the interiors.
By using a bottom-up reconstruction technique for non-minimally coupled scalar-tensor theories, we realize the Einstein frame attractor cosmologies in the $Ω(ϕ)$-Jordan frame. For our approach, what is needed for the reconstruction method to work is the functional form of the non-minimal coupling $Ω(ϕ)$ and of the scalar-to-tensor ratio, and also the assumption of the slow-roll inflation in the $Ω(ϕ)$-Jordan frame. By appropriately choosing the scalar-to-tensor ratio, we demonstrate that the observational indices of the attractor cosmologies can be realized directly in the $Ω(ϕ)$-Jordan frame.…
We study dynamics of non-minimally coupled scalar field cosmological models with Higgs-like potentials and a negative cosmological constant. In these models the inflationary stage of the Universe evolution changes into a quasi-cyclic stage of the Universe evolution with oscillation behaviour of the Hubble parameter from positive to negative values. Depending on the initial conditions the Hubble parameter can perform either one or several cycles before to become negative forever.
We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-minimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow roll $ε$ parameter. We regulate the infrared by matching onto a pre-inflationary radiation era. We find a large late time backreaction when the nonminimal coupling $ξ$ is negative (in which case the scalar exhibits a negative mass term during inflation). The one-loop quantum backreaction becomes significant today for moderately small non-minimal couplings, $…
We consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find that at the curvature singularity the speed of light goes to infinity while the gravitational constant vanishes. This corresponds to the Newton's Mechanics limit represented by one of the vertex of the Bronshtein-Zelmanov-Okun cube. The cosmological evolution includes both the pre-big-bang and post-big-bang phases separated by the curvature singula…
We obtain general solutions for some flat Friedmann universes filled with a scalar field in induced gravity models and models including the Hilbert-Einstein curvature term plus a scalar field conformally coupled to gravity. As is well known, these models are connected to minimally coupled models through the combination of a conformal transformation and a transformation of the scalar field. The explicit forms of the self-interaction potentials for six exactly solvable models are presented here. We obtain the general solution for one of the integrable models, namely, the induced gravity model wi…
Cosmology with a Non-minimally Coupled Dark Matter Fluid II. Cosmological Perturbations
SISSA - International School for Advanced Studies（国际高等研究院）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；INAF, IRA - Istituto di Radioastronomia（意大利国家天体物理研究所射电天文学研究所）
We study structure formation in non-minimally coupled dark energy models, where there is a coupling in the Lagrangian between a quintessence scalar field and gravity via the Ricci scalar. We consider models with a range of different non-minimal coupling strengths and compare these to minimally coupled quintessence models with time-dependent dark energy densities. The equations of state of the latter are tuned to either reproduce the equation of state of the non-minimally coupled models or their background history. Thereby they provide a reference to study the unique imprints of coupling on str…
We compare theoretical predictions with observations for a class of cosmological models in which the dark energy component is modeled as a fermionic condensate, non-minimally coupled with the gravitational field and characterized by some specific self-interaction potentials. Our analysis is based on the Markov Chain Monte Carlo Method (MCMC) and employs different data sets. It turns out that with an appropriate choice of parameters our models are fully compatible with several observed data. We combine these parameter values with phase space analysis to deduce the features of the entire cosmic …
We consider two classes of non-minimally coupled inflation models; those with a quadratic coupling of the inflaton to gravity, and the `Universal Attractor' models where the coupling is connected to the potential. We make a detailed analysis of the attractor structure in the latter case, identifying a shift of the attractor from the Starobinsky point and determining conditions for approach to the attractor. We then assess the viability of the models under different interpretations of the BICEP2 experiment's detection of B-mode polarisation, finding strong constraints on the non-minimal couplin…
The $β$-exponential inflation is driven by a class of primordial potentials, derived in the framework of braneworld scenarios, that generalizes the well-known power law inflation. In this paper we update previous constraints on the minimal coupled $β$-exponential model [1] and extend the results also deriving the equations for the non-minimal coupled scenario. The predictions of both models are tested in light of the latest temperature and polarization maps of the Cosmic Microwave Background and clustering data. We also compare the predictions of these models with the standard $Λ$CDM cosmology…
In this paper we show that the baryon-to-photon ratio $η$ is in general not conserved before decoupling in non-minimally coupled theories of gravity. We use big-bang nucleosynthesis and cosmic microwave background limits on the baryon-to-photon ratio $η$ to derive new constraints on modified gravity theories with a universal non-minimal coupling between matter and curvature, showing that they rule out a specific class of models previously considered in the literature as a substitute for the dark matter. We also compare these new constraints with the ones obtained from the COBE-FIRAS limits on …
We study the phenomenology associated to non-minimally coupled dark matter. In particular, we consider the model where the non-minimal coupling arises from the formation of relativistic Bose-Einstein condensates in high density regions of dark matter [1]. This non-minimal coupling is of Horndeski type and leads to a local modification of the speed of gravity with respect to the speed of light. Therefore we can constrain the model by using the joint detection of GW170817 and GRB170817A. We show that the constraints obtained in this way are quite tight, if the dark matter field oscillates freely…
Cosmology of self-interacting three-forms is investigated. The minimally coupled canonical theory can naturally generate a variety of isotropic background dynamics, including scaling, possibly transient acceleration and phantom crossing. An intuitive picture of the cosmological dynamics is presented employing an effective potential. Numerical solutions and analytical approximations are provided for scenarios which are potentially important for inflation or dark energy.
We explore the inflationary phase of a scalar field with a kinetic term non-minimally coupled to gravity. We find that one of the slow-roll conditions is naturally consequence of the equation of motion of the scalar field. Thus, slow-roll conditions impose fewer constraints on potentials than other inflationary models. Moreover, it is demonstrated that the inflationary phase can be described by just one slow-roll parameter. By investigating the metric perturbations, it is shown that except for one potential, almost all potentials have the same pattern in the ($n_{s}$, $r$) plane. We provide an…
In this paper, we fully investigate cosmological scenarios in which dark matter is non-minimally coupled to an extra scalar degree of freedom. The interaction is realized by means of conformal and disformal terms in the transformed gravitational metric. Considering linear perturbation theory, we show that the growth rate of dark matter differs from the uncoupled case and that the well-known Kaiser formula undergoes modification. As a result, redshift space distortion measurements cease to be a direct probe of the linear growth rate of total matter, since the distortion factor has an extra, cou…
As an extension of Dvali-Gabadadze-Porrati (DGP) model, the Galileon theory has been proposed to explain the "self-accelerating problem" and "ghost instability problem". In this Paper, we extend the Galileon theory by considering a non-minimally coupled Galileon scalar with gravity. The statefinder analysis, $Om(z)$ diagnostic and constraint the model parameters have been investigate , we find $Ω_\text{m0}=0.263_{-0.031}^{+0.031}$, $n=1.53_{-0.37}^{+0.21}$ (at the $95\%$ confidence level) with $χ^2_{\text{min}}=473.376$. Further we show that due to the SNe Ia + BAO data ,our model behaves like…
This paper is devoted to the study of Noether gauge symmetries of $f(T)$ gravity minimally coupled with a canonical scalar field. We explicitly determine the unknown functions of the theory $f(T),V(ϕ), W(ϕ)$. We have shown that there are two invariants for this model, one of which defines the Hamiltonian $H$ under time invariance (energy conservation) and the other is related to scaling invariance. We show that the equation of state parameter in the present model can cross the cosmological constant boundary. The behavior of Hubble parameter in our model closely matches to that of $Λ$CDM model,…
