Inflationary cosmology and the late-time accelerated expansion of the universe in non-minimal Yang-Mills-$F(R)$ gravity and non-minimal vector-$F(R)$ gravity
Kazuharu Bamba, Shin'ichi Nojiri, Sergei D. Odintsov
备注：
21 pages, no figure, shortened version, accepted in PRD, misprints corrected
We study inflationary cosmology and the late-time accelerated expansion of the universe in non-minimal Yang-Mills (YM) theory, in which the YM field couples to a function of the scalar curvature. It is shown that power-law inflation can be realized due to the non-minimal YM field-gravitational coupling which maybe caused by quantum corrections. Moreover, it is demonstrated that both inflation and the late-time accelerated expansion of the universe can be realized in a modified YM-$F(R)$ gravity which is consistent with solar system tests. Furthermore, it is shown that this result can be realized also in a non-minimal vector-$F(R)$ gravity. In addition, we consider the duality of the non-minimal electromagnetic theory and that of the non-minimal YM theory, and also discuss the cosmological reconstruction of the YM theory.
It is stressed that the kinematical problems of the standard cosmological model can be solved by a phase of accelerated contraction of the cosmic scale factor. Such a behaviour is only a particular case of a more general ``pre-big-bang" inflationary scenario, arising naturally in a string cosmology context, and driven asymptotically by the free dilaton field without any self-interaction potential and/or vacuum contribution.
The description of the accelerated phases for the current and primordial cosmos has been obtained in the framework of Rényi cosmology. The results show that corrections to the Friedmann equations, originated from differences between Rényi and Bekenstein entropies, can describe both the current accelerated and inflationary eras. The effects of these corrections can be appointed to a hypothetical fluid which is classically unstable. Although inflation can be obtained in Rényi cosmology as the vacuum solution, the values found for the parameters of the hypothetical fluid which supports the curren…
We study the dynamics of the universe with a scalar field and an SU(2) non-Abelian Gauge (Yang-Mills) field. The scalar field has an exponential potential and the Yang-Mills field is coupled to the scalar field with an exponential function of the scalar field. We find that the magnetic component of the Yang-Mills field assists acceleration of the cosmic expansion and a power-law inflation becomes possible even if the scalar field potential is steep, which may be expected from some compactification of higher-dimensional unified theories of fundamental interactions. This power-law inflationary s…
The accelerated expansion of space during the period of cosmological inflation leads to trans-Planckian issues which need to be addressed. Most importantly, the physical wavelength of fluctuations which are studied at the present time by means of cosmological observations may well originate with a wavelength smaller than the Planck length at the beginning of the inflationary phase. Thus, questions arise as to whether the usual predictions of inflationary cosmology are robust considering our ignorance of physics on trans-Planckian scales, and whether the imprints of Planck-scale physics are at …
Reheating is an important part of inflationary cosmology. It describes the production of Standard Matter particles after the phase of accelerated expansion. We give a review of the reheating process, focusing 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 preheat…
We propose an explanation for the present accelerated expansion of the universe that does not invoke dark energy or a modification of gravity and is firmly rooted in inflationary cosmology.
The energy-momentum tensor coming from one-parameter effective Yang- Mills theory is here used to describe the matter-energy content of the homogeneous and isotropic Friedmann cosmology in its early stages. The behavior of all solutions is examined. Particularly, it is shown that only solutions corresponding to an open model allow the universe to evolve into an accelerated expansion. This result appears as a possible mechanism for an inflationary phase produced by a vector field. Further, depending on the value of some parameters characterizing the system, the resulting models are classified a…
The recent CMB data from Planck and BICEP2 observations have opened a new window for inflationary cosmology. In this Essay we compare three Starobinsky-like inflationary scenarios: (i) the original Starobinsky proposal; (ii) a family of dynamically broken SUGRA models; and (iii) a class of "decaying" vacuum $Λ(H)$ cosmologies. We then focus on the $Λ(H)$ variant, which spans the complete cosmic history of the universe from an early inflationary stage, followed by the "graceful exit" into the standard radiation regime, the matter epoch and, finally, the late-time accelerated expansion. Computin…
We present a simple generalisation of the $Λ$CDM model which on the one hand reaches very good agreement with the present day experimental data and provides an internal inflationary mechanism on the other hand. It is based on Palatini modified gravity with quadratic Starobinsky term and generalized Chaplygin gas as a matter source providing, besides a current accelerated expansion, the epoch of endogenous inflation driven by type III freeze singularity. It follows from our statistical analysis that astronomical data favors negative value of the parameter coupling quadratic term into Einstein-H…
A gauge-invariant, linear cosmological perturbation theory of an almost homogeneous and isotropic universe with dynamically evolving Newton constant G and cosmological constant $Λ$ is presented. The equations governing the evolution of the comoving fractional spatial gradients of the matter density, G and $Λ$ are thus obtained. Explicit solutions are discussed in cosmologies, featuring an accelerated expansion, where both G and $Λ$ vary according to renormalization group equations in the vicinity of an ultraviolet fixed point. Finally, a similar analysis is carried out in the late universe reg…
We present a new mechanism for inflation which exhibits a speed limit on scalar motion, generating accelerated expansion even on a steep potential. This arises from explicitly integrating out the short modes of additional fields coupled to the inflaton $ϕ$ via a dimension six operator, yielding an expression for the effective action which includes a nontrivial (logarithmic) function of $(\partialϕ)^2$. The speed limit appears at the branch cut of this logarithm arising in a large flavor expansion, similarly to the square root branch cut in DBI inflation arising in a large color expansion. Fina…
We investigate the possibility that the modified Yang-Mills theories can produce an accelerated cosmic expansion. We take into account some specific non-trivial solution of the modified Yang-Mills equation obtained by the author earlier, which allows us to build several modifications of accelerated cosmic expansion.
Within Yang-Mills gravity with translation group $T(4)$ in flat space-time, the invariant action involving quadratic translation gauge-curvature leads to quadrupole radiations which are shown to be consistent with experiments. The radiation power turns out to be the same as that in Einstein's gravity to the second-order approximation. We also discuss an interesting physical reason for the accelerated cosmic expansion based on the long-range Lee-Yang force of $U_{b}(1)$ gauge field associated with the established conservation law of baryon number. We show that the Lee-Yang force can be related …
We address how to construct an infinitely cyclic universe model. A major consideration is to make the entropy cyclic which requires the entropy to be reset to zero in each cycle expansion to turnaround, to contraction, to bounce, etc. Here we reset entropy at the turnaround by selecting the introverse (visible universe) from the extroverse which is generated by the accelerated expansion. In the model, the observed homogeneity is explained by the low entropy at the bounce, The observed flatness arises from the contraction together with the reduction in size between the expanding and contracting…
In this article, we want to check four inflation models, such as composite NJL inflation (NJLI), Glueball inflation(GI), super Yang-Mills inflation (SYMI), and Orientifold inflation (OI), with two conjectures of the swampland program: scalar weak gravity conjecture (SWGC) and strong scalar weak gravity conjecture (SSWGC) since all these models violate the dS swampland conjecture(DSC) but are compatible with further refining de Sitter swampland conjecture (FRDSSC) through manual adjustment of free parameters of the mentioned conjecture. We want to study the simultaneous compatibility of each mo…
The discovery of dark energy (DE) as the physical cause for the accelerated expansion of the Universe is the most remarkable experimental finding of modern cosmology. However, it leads to insurmountable theoretical difficulties from the point of view of fundamental physics. Inflation, on the other hand, constitutes another crucial ingredient, which seems necessary to solve other cosmological conundrums and provides the primeval quantum seeds for structure formation. One may wonder if there is any deep relationship between these two paradigms. In this work, we suggest that the existence of the …
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In this work we consider a heavy quark moving with constant proper acceleration in the vacuum of any four dimensional conformal field theory. We argue that the two-point function of its momentum fluctuations is exactly captured by the Bremsstrahlung function that gives the total radiated power. For the particular case of N=4 SU(N) SYM this function is exactly known, so in this case we obtain an explicit expression for the momentum diffusion coefficient, and check that various limits of this result are reproduced by probe computations in AdS_5. Finally, we evaluate this transport coefficient fo…
Starting from Einstein-Yang-Mills in higher dimensions with an instanton on a compact sphere, we dimensionally reduce to find an effective four-dimensional action describing "hilltop" inflation. Using recent CMB data, we analyse the parameter space of this model to search for viable set-ups. One unique feature of this class of inflationary models is that the value of the inflaton field, or alternatively, the size of the compact sphere, is stabilised dynamically during the inflationary process.
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Inflation is an early period of accelerated cosmic expansion, thought to be sourced by high energy physics. A key task today is to use the influx of increasingly precise observational data to constrain the plethora of inflationary models suggested by fundamental theories of interactions. This requires a robust theoretical framework for quantifying the predictions of such models; helping to develop such a framework is the aim of this thesis. We provide the first complete quantization of subhorizon perturbations for the well-motivated class of multi-field inflationary models with a non-trivial f…
It was recently pointed out that the fundamental Planck mass could be close to the TeV scale with the observed weakness of gravity at long distances being due the existence of new sub-millimeter spatial dimensions. In this picture the standard model fields are localized to a $(3+1)$-dimensional wall or ``3-brane''. We show that in such theories there exist attractive models of inflation that occur while the size of the new dimensions are still small. We show that it is easy to produce the required number of efoldings, and further that the density perturbations $δρ/ρ$ as measured by COBE can be…
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In a series of five lectures I review inflationary cosmology. I begin with a description of the initial conditions problems of the Friedmann-Robertson-Walker (FRW) cosmology and then explain how inflation, an early period of accelerated expansion, solves these problems. Next, I describe how inflation transforms microscopic quantum fluctuations into macroscopic seeds for cosmological structure formation. I present in full detail the famous calculation for the primordial spectra of scalar and tensor fluctuations. I then define the inverse problem of extracting information on the inflationary era…
Following our previous paper, Bergeron et al, Smooth quantum dynamics of the mixmaster universe, Phys. Rev. D 92, 061302(R) (2015), concerning the quantization of the vacuum Bianchi IX model and the Born-Huang-Oppenheimer framework, we present a further analysis of the dynamical properties of the model. Consistently with the deep quantum regime, we implement the harmonic approximation of the anisotropy potential. We thus obtain manageable dynamical equations. We study the quantum anisotropic oscillations during the bouncing phase of the universe. Neglecting the backreaction from transitions be…
We consider a single field governed expansion of the universe from a five dimensional (5D) vacuum state. Under an appropiate change of variables the universe can be viewed in a effective manner as expanding in 4D with an effective equation of state which describes different epochs of its evolution. In the example here worked the universe fistly describes an inflationary phase, followed by a decelerated expansion. Thereafter, the universe is accelerated and describes a quintessential expansion to finally, in the future, be vacuum dominated.
The theory of cosmological perturbations has become a cornerstone of modern quantitative cosmology since it is the framework which provides the link between the models of the very early Universe such as the inflationary Universe scenario (which yield causal mechanisms for the generation of fluctuations) and the wealth of recent high-precision observational data. In these lectures, I provide an overview of the classical and quantum theory of cosmological fluctuations. Crucial points in both the current inflationary paradigm of the early Universe and in some proposed alternatives are that, first…
Inflationary predictions based on the linear theory of cosmological perturbations are related to the two point function of a (second quantized) real scalar free field during the accelerated stage. Such a two point function is finite, in contrast with its coincidence limit, which is divergent due to the ultraviolet divergences proper of field theory. We therefore argue that predictions of most of the inflationary models do not necessarily need a regularization scheme to leading order, i.e. tree level, which is required instead for non-linear corrections or calculations involving the energy-mome…
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The inflationary scenarios suggested by the duality properties of string cosmology in the Brans-Dicke (or String) frame are shown to correspond to accelerated contraction (deflation) when Weyl-transformed to the Einstein frame. We point out that the basic virtues of inflation (solving the flatness and horizon problems, amplifying vacuum fluctuations, etc.) have physically equivalent counterparts in the deflationary (Einstein-frame) picture. This could be the answer to some objections recently raised to superstring cosmology.
We study and estimate probabilistic predictions for the duration of the preinflationary and slow-roll phases after the bounce in loop quantum cosmology, determining how the presence of radiation in the prebounce phase affects these results. We present our analysis for different classes of inflationary potentials that include the monomial power-law chaotic type of potentials, namely, for the quadratic, quartic and sextic potentials and also for a Higgs-like symmetry breaking potential, considering different values for the vacuum expectation value in the latter case. We obtain the probability de…
The mechanism of the initial inflationary scenario of the universe and of its late-time acceleration can be described by assuming the existence of some gravitationally coupled scalar fields $ϕ$, with the inflaton field generating inflation and the quintessence field being responsible for the late accelerated expansion. Various inflationary and late-time accelerated scenarios are distinguished by the choice of an effective self-interaction potential $V(ϕ)$, which simulates a temporarily non-vanishing cosmological term. In this work, we present a new formalism for the analysis of scalar fields i…
The introduction of a delay in the Friedmann equation of cosmological evolution is shown to result in the very early universe undergoing the necessary accelerated expansion in the usual radiation (or matter) dominated phase. Occurring even without a violation of the strong energy condition, this expansion slows down naturally to go over to the decelerated phase, namely the standard Hubble expansion. This may obviate the need for a scalar field driven inflationary epoch.
We propose a cosmological model in which the universe undergoes an endless sequence of cosmic epochs each beginning with a `bang' and ending in a `crunch.' The temperature and density are finite at each transition from crunch to bang. Instead of having an inflationary epoch, each cycle includes a period of slow accelerated expansion (as recently observed) followed by slow contraction. The combination produces the homogeneity, flatness, density fluctuations and energy needed to begin the next cycle.
We study the Einstein Yang-Mills Higgs equations in the $SO(3)$ representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in…
In the theories described by a volume normalized action functional, an arbitrary cosmological constant is eliminated from the physical picture of our Universe, and dynamical alternatives must be responsible for today's accelerated expansion as well as for the conjectured early-time inflation in the Universe. A few well-known such scenarios realized by a single homogeneous scalar field are examined in this new context, and their diverse fates are elucidated. Typical inflationary models are not affected at the level of the background evolution, and also give rise to the scalar perturbations equi…
An accelerated universe should naturally have a vacuum energy density determined by its dynamical curvature. The cosmological constant is most likely a temporary description of a dynamical variable that has been drastically evolving from the early inflationary era to the present. In this Essay we propose a unified picture of the cosmic history implementing such an idea, in which the cosmological constant problem is fixed at early times. All the main stages, from inflation and its ("graceful") exit into a standard radiation regime, as well as the matter and dark energy epochs, are accounted for…
We employ Riesz's fractional derivative into the Wheeler--DeWitt equation for a closed de Sitter geometry and obtain the no-boundary and tunneling wavefunctions. From the corresponding probability distributions, the event horizon of the nucleated universe can be a fractal surface with dimensions between $2\leq D<3$. Concretely, the tunneling wavefunction favors fractal dimensions less than $2.5$ and an accelerated power-law phase. Differently, the no-boundary proposal conveys fractal dimensions close to $3$, with the universe instead entering a decelerated phase. Subsequently, we extend our di…
A non-abelian $SU(2)$ gauge field with a non-minimal Horndeski coupling to gravity gives rise to a de Sitter solution followed by a graceful exit to a radiation-dominated epoch. In this Horndeski Yang-Mills (HYM) theory we derive the second-order action for tensor perturbations on the homogeneous and isotropic quasi de Sitter background. We find that the presence of the Horndeski non-minimal coupling to the gauge field inevitably introduces ghost instabilities in the tensor sector during inflation. Moreover, we also find Laplacian instabilities for the tensor perturbations deep inside the Hubb…
We propose new mechanism for inflation using classical SU(2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflatio…
Motivated by the properties of matter quantum fields in curved space-times, we work out a gravity theory that combines the Born-Infeld gravity Lagrangian with an $f(R)$ piece. To avoid ghost-like instabilities, the theory is formulated within the Palatini approach. This construction provides more freedom to address a number of important questions such as the dynamics of the early universe and the cosmic accelerated expansion, among others. In particular, we consider the effect that adding an $f(R)=a R^2$ term has on the early-time cosmology. We find that bouncing solutions are robust against t…
The problem of a heavy quark-anti-quark pair which have constant eternal acceleration in opposite directions in the vacuum of deconfined maximally supersymmetric Yang-Mills theory is studied both in perturbation theory and at strong coupling using AdS/CFT. Perturbation theory is summed to obtain what is conjectured to be an exact result. It is shown to agree with a particular prescription for computing the disc amplitude in the string theory dual and it yields a value $s=\sqrtλ$ for the entanglement entropy of the quark and anti-quark.
This thesis is dedicated to the study of inflationary scenarios based on string theory. Inflation is a brief period of accelerated expansion in the very early Universe which gives natural explanations for problems of the Standard Big Bang Model (SBBM) of cosmology. The phenomenological success of inflation provides the motivation for numerous efforts to establish its connection with particle physics. As a promising contender for a unified theory at very high energy scales, string theory is an obvious framework to look for the theoretical foundations of inflation; we therefore try to determine …
We point out that a simple inflationary model in which the axionic inflaton couples to a pure Yang-Mills theory may give the scalar spectral index (n_s) and tensor-to-scalar ratio (r) in complete agreement with the current observational data.
We consider quantum \cal{N} = 4 super Yang-Mills theory interacting in a covariant way with \cal{N} = 4 conformal supergravity. The induced large N effective action for such a theory is calculated on a dilaton-gravitational background using the conformal anomaly found via AdS/CFT correspondence. Considering such an effective action as a quantum correction to the classical gravity action we study quantum cosmology. In particular, the effect from dilaton to the scale factor (which without dilaton corresponds to the inflationary universe) is investigated. It is shown that, dependent on the initia…
We investigate cosmological scenarios in the theory of gravity with the scalar field possessing a non-minimal kinetic coupling to the curvature. It is shown that the kinetic coupling provides an essentially new inflationary mechanism. Namely, at early cosmological times the domination of coupling terms in the field equations guarantees the quasi-De Sitter behavior of the scale factor: $a(t)\propto e^{H_κ t}$ with $H_κ=1/\sqrt{9κ}$, where $κ\simeq 10^{-74}$ sec$^2$ is the coupling parameter. The primary inflationary epoch driven by non-minimal kinetic coupling comes to the end at $t_f \simeq 10…
We study quintessential inflation using a generalized exponential potential $V(ϕ)\propto exp(-λϕ^n/Mpl^n), n>1$, the model admits slow-roll inflation at early times and leads to close-to-scaling behaviour in the post inflationary era with an exit to dark energy at late times. We present detailed investigations of the inflationary stage in the light of the Planck 2015 results, study post-inflationary dynamics and analytically confirm the existence of an approximately scaling solution. Additionally, assuming that standard massive neutrinos are non-minimally coupled, makes the field $ϕ$ dominant …
In this paper we study some models where non-Abelian gauge vector fields endowed with a SU(2) group representation are the unique source of inflation and dark energy. These models were first introduced under the name of gaugeflation and gaugessence, respectively. Although several realizations of these models have been discussed, not all available parameters and initial conditions are known. In this work, we use a dynamical system approach to find the full parameter space of the massive version of each model. In particular, we found that the inclusion of the mass term increases the length of th…
We study tensor modes in pure natural inflation (arXiv:1706.08522), a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the theta-angle dependence of the vacuum energy.
