We study the future evolution of quintessence/phantom dominated epoch in modified $F(R)$-gravity which unifies the early-time inflation with late-time acceleration and which is consistent with observational tests. Using the reconstruction technique it is demonstrated that there are models where any known (Big Rip, II, III or IV Type) singularity may classically occur. From another side, in Einstein frame (scalar-tensor description) only IV Type singularity occurs. Near the singularity the classical description breaks up, it is demonstrated that quantum effects act against the singularity and may prevent its appearance. The realistic $F(R)$-gravity which is future singularity free is proposed. We point out that additional modification of any $F(R)$-gravity by the terms relevant at the early universe is possible, in such a way that future singularity does not occur even classically.
We consider modified $f(R)$ gravity which may unify $R^m$ early-time inflation with late-time $Λ$CDM epoch. It is shown that such model passes the local tests (Newton law, stability of Earth-like gravitational solution, very heavy mass for additional scalar degree of freedom) and suggests the realistic alternative for General Relativity. Various scenarios for future evolution of $f(R)$ $Λ$CDM era are discussed.
We suggest two realistic f(R) and one F(G) modified gravities which are consistent with local tests and cosmological bounds. The typical property of such theories is the presence of the effective cosmological constant epochs in such a way that early-time inflation and late-time cosmic acceleration are naturally unified within single model. It is shown that classical instability does not appear here and Newton law is respected. Some discussion of possible anti-gravity regime appearence and related modification of the theory is done.
We review the recent attempts of unifying inflation with quintessence. It appears natural to join the two ends in the framework of brane world cosmology. The models of quintessential inflation belong to the class of {\it non-oscillatory} models for which the mechanism of conventional reheating does not work. Reheating through gravitational particle production is inefficient and leads to the excessive production of relic gravity waves which results in the violation of nucleosynthesis constraint. The mechanism of {\it instant preheating} is quite efficient and is suitable for brane world quintes…
We propose a simple model where a {\it gauge invariant inflaton} is responsible for cosmic inflation and generates the seed for structure formation, while its relic {\it thermal} abundance explains the missing matter of the universe in the form of cold dark matter. The inflaton self-coupling also explains the observed neutrino masses. All the virtues can be attained in a minimal extension of the Standard Model gauge group around the TeV scale. We can also unveil these properties of an inflaton in forthcoming space and ground based experiments.
The review of basic cosmological properties of four-dimensional F(R)-gravity, including FRW equations of motion and its accelerating solutions, generalized fluid and scalar-tensor representation of the theory is done. Cosmological reconstruction equation is written and conditions for stability of cosmological solution are discussed. The overview of realistic F(R)-models unifying inflation with dark energy epoch is made. The avoidance of finite-time future singularities in such theories via the introduction of R^2-term is studied. New realistic non-singular F(R)-gravity unifying early-time infl…
The unifying approach to early-time and late-time universe based on phantom cosmology is proposed. We consider gravity-scalar system which contains usual potential and scalar coupling function in front of kinetic term. As a result, the possibility of phantom-non-phantom transition appears in such a way that universe could have effectively phantom equation of state at early time as well as at late time. In fact, the oscillating universe may have several phantom and non-phantom phases. As a second model we suggest generalized holographic dark energy where infrared cutoff is identified with combi…
Scalar fields appear in many cosmological models, in particular in order to provide explanations for dark energy and inflation, but also to emulate dark matter. In this paper, we show that it is possible for a scalar field to replace simultaneously dark matter, dark energy and inflation by assuming the existence of a non-minimal coupling to gravity, a Mexican hat potential, and a spontaneous symmetry breaking before inflation. After inflation, the scalar field behaves like a dark fluid, mimicking dark energy and dark matter, and has a dark matter behaviour similar to fuzzy dark matter.
We study FRW cosmology for a non-linear modified F(R) Horava-Lifshitz gravity which has a viable convenient counterpart. A unified description of early-time inflation and late-time acceleration is possible in this theory, but the cosmological dynamic details are generically different from the ones of the convenient viable F(R) model. Remarkably, for some specific choice of parameters they do coincide. The emergence of finite-time future singularities is investigated in detail. It is shown that these singularities can be cured by adding an extra, higher-derivative term, which turns out to be qu…
In this work we shall present models of $F(R)$ gravity which realize in a unified way the inflationary era along with a post-inflationary early dark energy era, with the late-time dark energy era. We shall use two approach methods in order to realize the unified cosmological eras, firstly we specify a Hubble rate which may describe the three distinct acceleration eras, and then by using well known $F(R)$ gravity reconstruction techniques, we shall find the differential equation which may yield the $F(R)$ gravity that realizes the cosmologies. In our second approach, we shall present in a quali…
A unified multi scalar field model with three flat regions is discussed. The three flat regions are the inflation, early and late dark energy epochs. The potential is obtained by a spontaneous breaking of scale invariance generated by Non Riemannian Measures of integration (or Two Measures Theories (TMT)).We define the scale invariant couplings of the scalar fields to the different measures through exponential potentials. Spontaneous breaking of scale invariance takes place when integrating the fields that define the measures. When going to the Einstein frame we obtain: (i) An effective potent…
Extendibility of inflationary spacetimes with flat spatial geometry is investigated. We find that the past boundary of an inflationary spacetime becomes a so-called parallely propagated curvature singularity if the ratio $\dot{H}/a^2$ diverges at the boundary, where $\dot{H}$ and $a$ represent the time derivative of the Hubble parameter and the scale factor, respectively. On the other hand, if the ratio $\dot{H}/a^2$ converges, then the past boundary is regular and continuously extendible. We also develop a method to judge the continuous ($C^0$)extendibility of spacetime in the case of slow-ro…
We provide a theoretical model of $F(R)$ gravity in which it is possible to describe in a unified way inflation, an early and a late dark energy era, in the presence of a light axion particle which plays the role of the dark matter component of the Universe. Particularly, the early-time phenomenology is dominated by an $R^2$ term, while the presence of the other terms $f(R)$ ensure the occurrence of the early and late-time dark energy eras. The inflationary phenomenology is compatible with the Planck 2018 data for inflation, while the late-time dark energy era is compatible with the Planck 201…
We review some recent trends in the inflationary model building, the supersymmetry (SUSY) breaking, the gravitino Dark Matter (DM) and the Primordial Black Holes (PBHs) production in supergravity. The Starobinsky inflation can be embedded into supergravity when the inflaton belongs to the massive vector multiplet associated with a (spontaneously broken) $U(1)$ gauge symmetry. The SUSY and R-symmetry can be also spontaneously broken after inflation by the (standard) Polonyi mechanism. Polonyi particles and gravitinos are super heavy and can be copiously produced during inflation via the Schwing…
A minimal extension of the Standard Model (SM) with a single new mass scale and providing a complete and consistent picture of particle physics and cosmology up to the Planck scale is presented. We add to the SM three right-handed SM-singlet neutrinos, a new vector-like color triplet fermion and a complex SM singlet scalar $σ$ that stabilises the Higgs potential and whose vacuum expectation value at $\sim 10^{11}$ GeV breaks lepton number and a Peccei-Quinn symmetry simultaneously. Primordial inflation is produced by a combination of $σ$ (non-minimally coupled to the scalar curvature) and the …
Based on the formulation of the reconstruction for the k-essence model, which was recently proposed in arXiv:1001.0220 [hep-th], we explicitly construct cosmological model to unifying the late-time acceleration and the inflation in the early universe.
We present some cosmological models which unify the late and early-time acceleration eras with the radiation and the matter domination era, and we realize the cosmological models by using the theoretical framework of $F(R)$ gravity. Particularly, the first model unifies the late and early-time acceleration with the matter domination era, and the second model unifies all the evolution eras of our Universe. The two models are described in the same way at early and late times, and only the intermediate stages of the evolution have some differences. Each cosmological model contains two Type IV sin…
It is shown that the inflationary paradigm admits quantum complete extensions of space-time. The extended inflationary spacetimes still have geodesic borders, but quantum fields are prohibited from migrating across these borders by their evolution semigroups. The geodesic singularities lurking across the borders lack a physical description because the evolution semigroups give vanishing probabilistic support to quantum fields for populating regions bordering on these singularities. As an example, anisotropic Bianchi type-I cosmologies are shown to be quantum complete preludes to inflation. The…
The four-form field recently considered by Hawking and Turok couples naturally to a charged membrane, across which the effective cosmological constant has a discontinuity. We present instantons for the creation of an open inflationary universe surrounded by a membrane. They can also be used to describe the nucleation of a membrane on a pre-existing inflationary background. This process typically decreases the value of the effective cosmological constant and may lead to a novel scenario of eternal inflation. Moreover, by coupling the inflaton field to the membrane, the troublesome singularities…
We find that general relativity can be naturally free of cosmological singularities. Several nonsingular models are currently available that either assume ad hoc matter contents, or are nonsingular only over a sector of solution space of zero measure, or depart drastically from general relativity at high energies. After much uncertainty over whether cosmological inflation could help solve the initial-singularity problem, the prevailing belief today is that general relativistic cosmology, with inflation or without, is endemically singular. This belief was reinforced by recent singularity theore…
We provide a detailed quantitative description of singular inflation. Its close analogy with finite-time future singularity which is associated to dark energy era is described. Calling and classifying the singularities of such inflation as finite-time cosmological singularities we investigate their occurrence, with special emphasis on the Type IV singularity. The study is performed in the context of a general non-canonical scalar-tensor theory. In addition, the impact of finite time singularities on the slow-roll parameters is also investigated. Particularly, we study three cases, in which the…
A general framework for effective theories propagating two tensor and one scalar degrees of freedom is investigated. Geometrically, it describes dynamical foliation of spacelike hypersurfaces coupled to a general background, in which the scalar mode encodes the fluctuation of the hypersurfaces. Within this framework, various models in the literature---including $k$-essence, Horndeski theory, the effective field theory of inflation, ghost condensate as well as the Hořava gravity---get unified. Our framework generalizes the Horndeski theory in the sense that, it propagates the correct number of …
We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, $V(ϕ)=Aϕ^{n}$, with $0<n<1$ and $A>0$ always develops a finite-time singularity at which the Hubble rate and its first derivative are finite, but its second derivative diverges. These are the first examples of cosmological models with realistic matter sources that possess weak singularities of 'sudden' type. We also show that a large class of models with even weaker singularities exist for non-integer $n>1$. More precisely, if $k<n<k+1$ where $k$ is a positive integer then the first diverge…
We discuss excitation of string oscillation modes by an initial singularity of inflation. The initial singularity of inflation is known to occur with a finite Hubble parameter, which is generally lower than the string scale, and hence it is not clear that stringy effects become significant around it. With the help of Penrose limit, we find that infinitely heavy oscillation modes get excited when a singularity is strong in the sense of Krolak's classification. We demonstrate that the initial singularities of Starobinsky and hill top inflation, assuming the slow roll inflation to the past infini…
We study $F(R)$ modified gravity models which are capable of driving the accelerating epoch of the Universe at the present time whilst not destroying the standard Big Bang and inflationary cosmology. Recent studies have shown that a weak curvature singularity with $|R|\to\infty$ can arise generically in viable $F(R)$ models of present dark energy (DE) signaling an internal incompleteness of these models. In this work we study how this problem is cured by adding a quadratic correction with a sufficiently small coefficient to the $F(R)$ function at large curvatures. At the same time, this correc…
Using the fluid representation, we formulate the conditions for the appearance of all four types finite-time future singularity in modified gravity in accelerating FRW universe. It stressed that number of standard quintessence/phantom DE theories (including scalar, fluid, DBI ones, etc) brings the accelerating cosmology to future singularity precisely in the same way as singular modified gravity DE. The viable non-singular modified gravity unifying the early-time inflation with late-time acceleration is considered. It is shown that adding such non-singular theory to another realistic singular …
Motivated by the fact that the pre-inflationary era may evolve in an exotic way, in this work we formalize anisotropic evolution in the context of modified gravity, focusing on pre-inflationary and near the vicinity of the inflationary epochs. We specialize on specific metrics like Bianchi and Taub and we formalize the inflationary theory in vacuum $F(R)$ gravity, in $F(R)$ gravity with an extra scalar field and in Gauss-Bonnet gravity. We discuss the qualitative effects of the anisotropies on the evolution of the Universe and also we consider several specific solutions, like the de Sitter sol…
To gain insight in the quantum nature of cosmological singularities, we study anisotropic Kasner solutions in gauge/gravity duality. The dual description of the bulk evolution towards the singularity involves N = 4 super Yang-Mills on the expanding branch of deformed de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlators show a strong signature of the singularity around horizon scales and decay at large boundary separation at different rates in different directions. Mo…
We consider the reconstruction technique in theories with a single or multiple (phantom and/or canonical) scalar fields. With the help of several examples, it is demonstrated explicitly that the universe expansion history, unifying early-time inflation and late-time acceleration, can be realized in scalar-tensor gravity. This is generalized to the theory of a scalar field coupled non-minimally to the curvature and to a Brans-Dicke-like theory. Different examples of unification of inflation with cosmic acceleration, in which de Sitter, phantom, and quintessence type fields play the fundamental …
We review cosmology in non-minimal Yang-Mills/Maxwell theory, in which the Yang-Mills/electromagnetic field couples to a function of the scalar curvature. We show that power-law inflation can be realized due to the non-minimal gravitational coupling of the Yang-Mills field which may be caused by quantum corrections. Moreover, we study non-minimal vector model in the framework of modified gravity and demonstrate that both inflation and the late-time accelerated expansion of the universe can be realized. We also discuss the cosmological reconstruction of the Yang-Mills theory. Furthermore, we in…
Brane cosmology presents many interesting possibilities including: phantom acceleration (w<-1), self-acceleration, unification of dark energy with inflation, transient acceleration, loitering cosmology, new singularities at which the Hubble parameter remains finite, cosmic mimicry, etc. The existence of a time-like extra dimension can result in a singularity-free cyclic cosmology.
We review the accelerating (mainly, dark energy) cosmologies in modified gravity. Special attention is paid to cosmologies leading to finite-time future singularities in $F(R)$, $F(G)$ and $\mathcal{F}(R,G)$ modified gravities. The removal of the finite-time future singularities via addition of $R^2$-term which simultaneously unifies the early-time inflation with late-time acceleration is also briefly mentioned. Accelerating cosmology including the scenario unifying inflation with dark energy is considered in $F(R)$ gravity with Lagrange multipliers. In addition, we examine domain wall solutio…
We demonstrate that finite time singularities of Type IV can be consistently incorporated in the Universe's cosmological evolution, either appearing in the inflationary era, or in the late-time regime. While using only one scalar field instabilities can in principle occur at the time of the phantom-divide crossing, when two fields are involved we are able to avoid such instabilities. Additionally, the two-field scalar-tensor theories prove to be able to offer a plethora of possible viable cosmological scenarios, at which various types of cosmological singularities can be realized. Amongst othe…
A unified description of early-time inflation with the current cosmic acceleration is achieved by means of a new theory that uses a quadratic model of gravity, with the inclusion of an exponential $F(R)$-gravity contribution for dark energy. High-curvature corrections of the theory come from higher-derivative quantum gravity and yield an effective action that goes beyond the one-loop approximation. It is shown that, in this theory, viable inflation emerges in a natural way, leading to a spectral index and tensor-to-scalar ratio that are in perfect agreement with the most reliable Planck result…
ACT-DR6 consistent inflation in generalised entropic cosmology and $f(Q)$ gravity
Shanghai Jiao Tong University（上海交通大学）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；Nagoya University（名古屋大学）；Institució Catalana de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚研究与高等研究学院）
We investigate in which cases a singular evolution with a singularity of Type IV, can be consistently incorporated in deformations of the $R^2$ inflationary potential. After demonstrating the difficulties that the single scalar field description is confronted with, we use a general two scalar fields model without other matter fluids, to describe the Type IV singular evolution, with one of the two scalar fields being canonical. By appropriately choosing the non-canonical scalar field, we show that the canonical scalar field corresponds to a potential that is nearly the $R^2$ inflation potential…
A specific Horndeski scalar-gravity mimetic model is investigated within a FLWR space-time. The mimetic scalar field is implemented via a Lagrangian multiplier, and it is shown that the model has equations of motion formally similar to the original simpler mimetic matter model of Chamseddine-Mukhanov-Vikman. Several exact solutions describing inflation, bounces, future time singularities are presented and discussed.
We study inflation as a "cosmic" renormalization-group flow. The flow, which encodes the dependence on the background metric, is described by a running coupling $α$, which parametrizes the slow roll, a de Sitter free, analytic beta function and perturbation spectra that are RG invariant in the superhorizon limit. Using RG invariance as a guiding principle, we classify the main types of flows according to the properties of their spectra, without referring to their origins from specific actions or models. Novel features include spectra with essential singularities in $α$ and violations of the re…
We consider a probe codimension-2 brane inflation scenario in a warped six-dimensional flux compactification. Our background model is Salam-Sezgin gauged supergravity with codimension-2 brane sources, which preserve N=1 supersymmetry. The model has a modulus, which is stabilised by means of a cap regularisation of the codimension-2 singularities, with appropriate dilaton potentials on the ring interface of the caps with the bulk. We discuss the cosmological evolution of the world-volume of a probe codimension-2 brane when it moves along the radial direction of the internal space. In order to h…
Unlike crushing singularities, the so-called Type IV finite-time singularity offers the possibility that the Universe passes smoothly through it, without any catastrophic effects. Then the question is if the effects of a Type IV singularity can be detected in the process of cosmic evolution. In this paper we address this question in the context of $F(R)$ gravity. As we demonstrate, the effects of a Type IV singularity appear in the Hubble flow parameters, which determine the dynamical evolution of the cosmological system. So we study various inflation models incorporating a Type IV singularity…
We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom…
We consider the thermodynamical behavior of Banks-Zaks theory close to the conformal point in a cosmological setting. Due to the anomalous dimension, the resulting pressure and energy density deviate from that of radiation and result in various interesting cosmological scenarios. Specifically, for a given range of parameters one avoids the cosmological singularity. We provide a full "phase diagram" of possible Universe evolution for the given parameters. For a certain range of parameters, the thermal averaged Banks-Zaks theory alone results in an exponentially contracting universe followed by …
The one-loop effective action for non-minimal scalar modified gravity on de Sitter background with a constant scalar field is found. The corresponding induced cosmological constant is evaluated. It is shown that quantum effects in non-minimal modified gravity may induce an early-time de Sitter universe even in the situation when such solution does not occur on the classical level. Classical reconstruction of the theory is presented in such a way that the resulting theory has a cosmological solution unifying early-time inflation with late-time acceleration.
We review recent progress on cosmological issues and theoretical properties of modified gravity theories. In particular, we explicitly explore the conformal transformation, the Starobinsky inflation, and a unified scenario of inflation and late time acceleration in $F(R)$ gravity and $F(T)$ gravity (extended teleparallel gravity). Furthermore, we examine neutron stars and the hyperon problem in $F(R)$ gravity. Moreover, for loop quantum cosmology (LQC), the natures of finite-time future singularities in $F(T)$ gravity are presented. In addition, we investigate $F(T)$ gravity theories from the …
We investigate how the gravitational baryogenesis mechanism can potentially constrain the form of a Type IV singularity. Specifically, we study two different models with interesting phenomenology, that realize two distinct Type IV singularities, one occurring at the end of inflation and one during the radiation domination era or during the matter domination era. As we demonstrate, the Type IV singularities occurring at the matter domination era or during the radiation domination era, are constrained by the gravitational baryogenesis, in such a way so that these do not render the baryon to entr…
