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 singularity occurs during the inflationary era, at the end, and also we study the case that the singularity occurs much more later than inflation ends. Using the obtained slow-roll parameters, for each case, we calculate explicitly the spectral index of primordial curvature perturbations $n_s$, the associated running of the spectral index $a_s$ and of the scalar-to-tensor ratio $r$ and compare the resulting values to the Planck and BICEP2 data. As we demonstrate, in some cases corresponding to the Type IV singularity, there might be the possibility of agreement with the observational data, when the singularity occurs at the end, or after inflation. However, absolute concordance of all observational indices is not achieved. On the contrary, if the singularity occurs during the inflationary era, this is catastrophic for the theory, since the observational indices become divergent. We also show how a Type IV singularity may be consistently accommodated in the Universe's late time evolution.
Accelerating dynamics from Born-Infeld-$f(R)$ gravity are studied in a simplified conformal approach without matter. Explicit unification of inflation with late-time acceleration is realized within this singular inflation approach, which is similar to Odintsov-Oikonomou singular $f(R)$ inflation. Our model turns out to be consistent with the latest release of Planck data.
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…
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 …
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 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…
In this paper we consider a unique model of inflation where the universe undergoes rapid asymmetric oscillations, each cycle lasting millions of Planck time. Over many-many cycles the space-time expands to mimic the standard inflationary scenario. Moreover, these rapid oscillations leave a distinctive periodic signature in ln(k) in the primordial power spectrum, where k denotes the comoving scale. The best fit parameters of the cyclic-inflation model provides a very good fit to the 7-year WMAP data.
We consider a polymer quantization of a free massless scalar field in a homogeneous and isotropic cosmological spacetime. This quantization method assumes that field translations are fundamentally discrete, and is related to but distinct from that used in loop quantum gravity. The semi-classical Friedman equation yields a universe that is non-singular and non-bouncing, without quantum gravity. The model has an early de Sitter-like inflationary phase with sufficient expansion to resolve the horizon and entropy problems, and a built in mechanism for a graceful exit from inflation.
We study gravitational collapse of a charged black hole in f(R) gravity using double-null formalism. We require cosmological stability to f(R) models; we used the Starobinsky model and the R + (1/2)cR^2 model. Charged black holes in f(R) gravity can have a new type of singularity due to higher curvature corrections, the so-called f(R)-induced singularity, although it is highly model-dependent. As the advanced time increases, the internal structure will approach the Cauchy horizon, which may not be an inner apparent horizon. There is mass inflation as one approaches the Cauchy horizon and hence…
We study models with a generalized inhomogeneous equation of state fluids, in the context of singular inflation, focusing to so-called Type IV singular evolution. In the simplest case, this cosmological fluid is described by an equation of state with constant $w$, and therefore a direct modification of this constant $w$ fluid, is achieved by using a generalized form of an equation of state. We investigate from which models with generalized phenomenological equation of state, a Type IV singular inflation can be generated and what the phenomenological implications of this singularity would be. W…
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 investigate how a Type IV future singularity can be included in the cosmological evolution of a well-known exponential model of inflation. In order to achieve this we use a two scalar field model, in the context of which the incorporation of the Type IV singularity can be consistently done. In the context of the exponential model we study, when a Type IV singularity is included in the evolution, an instability occurs in the slow-roll parameters, and in particular on the second slow-roll parameter. Particularly, if we abandon the slow-roll condition for both the scalars we shall use, then th…
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 possibility to have singular accelerated evolution in the context of $F(R)$ bimetric gravity is investigated. Particularly, we study two singular models of cosmological evolution, one of which is a singular modified version of the Starobinsky $R^2$ inflation model. As we demonstrate, for both models in some cases, the slow-roll parameters become singular at the Type IV singularity, a fact that we interpret as a dynamical instability of the theory under study. This dynamically instability may be an indicator of graceful exit from inflation and we thoroughly discuss this scenario and the int…
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 …
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 analytically derive a class of non-singular, static and spherically symmetric topological black hole metrics inF(R)-gravity. These have not a de Sitter core at their centre, as most model in standard General Relativity. We study the geometric properties and the motion of test particles around these objects. Since they have two horizons, the inner being of Cauchy type, we focus on the problem of mass inflation and show that it occurs except when some extremal conditions are met.
We investigate the early-time accelerated universe after the Big Bang. We pay attention to the dissipative properties of the inflationary universe in the presence of a soft type singularity, making use of the parameters of the generalized equation of state of the fluid. Flat Friedmann-Robertson-Walker metric is being used. We consider cosmological models leading to the so-called type IV singular inflation. Our obtained theoretical results are compared with observational data from the Planck satellite. The theoretical predictions for the spectral index turn out to be in agreement with the data,…
We investigate the dynamics of single and multiple scalar fields with exponential potentials, leading to power-law and assisted inflation, in loop quantum cosmology. Unlike in the classical theory, dynamical trajectories in loop quantum cosmology are generically non-singular, with a big bounce replacing classical big bang in the Planck regime. Post bounce, after a phase of super-inflation, dynamical trajectories evolve towards the classical attractor in the inflationary scenarios. Depending on the initial conditions, bounce is shown to occur in kinetic as well as potential dominated regimes. W…
We demonstrate that the intermediate inflation scenario, is a singular inflation cosmology, with the singularity at the origin $t=0$ being a pressure and energy density singularity and particularly a Type III singularity. Also, we show that the expanding phase of a singular bounce, can be identical to the intermediate inflation scenario, if the singular bounce has a Type III singularity at the origin. For the intermediate inflation scenario we examine the cosmological implications on the power spectrum in the context of various forms of modified gravity. Particularly we calculate the power spe…
In common relativistic models of gravitational collapse, the interior experiences a bubble-like local inflation, allowing radii to diverge rather than converge toward a singularity. This proves a conjecture of Shatskiy. At the horizon, the solution locally resembles the neck of a wormhole from the exterior to the interior. The implied limiting curvature is at the horizon not the Planck level.
The singularity in Hawking and Turok's model (hep-th/9802030) of open inflation has some appealing properties. We suggest that this singularity should be regularized with matter. The singular instanton can then be obtained as the limit of a family of ``no-boundary'' solutions where both the geometry and the scalar field are regular. Using this procedure, the contribution of the singularity to the Euclidean action is just 1/3 of the Gibbons-Hawking boundary term. Unrelated to this question, we also point out that gravitational backreaction improves the behaviour of scalar perturbations near 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 review here some recent results that show that inflationary cosmological models must contain initial singularities. We also present a new singularity theorem. The question of the initial singularity re-emerges in inflationary cosmology because inflation is known to be generically future-eternal. It is natural to ask, therefore, if inflationary models can be continued into the infinite past in a non-singular way. The results that we discuss show that the answer to the question is ``no.'' This means that we cannot use inflation as a way of avoiding the question of the birth of the Universe. W…
In this paper, we apply a method of reducing the dynamics of FRW cosmological models with the barotropic form of the equation of state to the dynamical system of the Newtonian type to detect the finite scale factor singularities and the finite-time singularities. In this approach all information concerning the dynamics of the system is contained in a diagram of the potential function $V(a)$ of the scale factor. Singularities of the finite scale factor manifest by poles of the potential function. In our approach the different types of singularities are represented by critical exponents in the p…
General non-singular accelerating cosmological solutions for an initial cosmic period of pure vacuum birth era are derived. This vacuum era is described by a varying cosmological "constant" suggested by the Renormalisation Group flow of Asymptotic Safety scenario near the ultraviolet fixed point. In this scenario, natural exit from inflation to the standard decelerating cosmology occurs when the energy scale lowers and the cosmological "constant" becomes insignificant. In the following period where matter is also present, cosmological solutions with characteristics similar to the vacuum case a…
We use the phenomenological approach to study properties of space-time in the vicinity of the Schwarzschild black-hole singularity. Requiring finiteness of the Schwarzschild-like metrics we come to the notion of integrable singularity that is, in a sense, weaker than the conventional singularity and allows the (effective) matter to pass to the white-hole region. This leads to a possibility of generating a new universe there. Thanks to the gravitational field of the singularity, this universe is already born highly inflated ('singularity-induced inflation') before the ordinary inflation starts.
A remarkable property of modern cosmology is that it allows for a special case of symmetry, consisting in the possibility of describing the early-time acceleration (inflation) and the late-time acceleration using the same theoretical framework. In this paper we consider various cosmological models corresponding to a generalized form for the equation of state for the fluid in a flat Friedmann -Robertson-Walker universe, emphasizing cases where the so-called type IV singular inflation is encountered in the future. This is a soft (non-crushing) kind of singularity. Parameter values for an inhomog…
Due to the accelerated expansion of the universe, the possibility of formation of singularities has changed from the classical Big Bang and Big Crunch singularities to include a number of new scenarios. In recent papers it has been shown that such singularities may appear in inflationary cosmological models with a fractional power scalar field potential. In this paper we enlarge the analysis of singularities in scalar field cosmological models by the use of generalised power expansions of their Hubble scalar and their scalar field in order to describe all possible models leading to a singulari…
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 m…
In [1] a new cosmological model is proposed with no big bang singularity in the past, though past geodesically incomplete. This model starts with an inflationary era, follows with a stiff matter dominated period and evolves to accelerated expansion in an asymptotically de Sitter regime in a realistic fashion. The big bang singularity is replaced by a directional singularity. This singularity cannot be reached by comoving observers, since it would take them an infinite proper time lapse to go back to it. On the contrary, observers with nonzero linear momentum have the singularity at finite prop…
In this paper, we examine a flat FLRW spacetime with a scalar field potential and show by applying Osgood's criterion to the Einstein field equations that all such models, irrespective of the particular choice of potential develop finite-time singularities. That is, we show that solutions to the field equations become singular in finite time, which can have important implications for the role of inflation in cosmological models. We further point out that a possible reason for this behaviour is that the solutions to the field equations in such inflationary scenarios do not obey global existence…
Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and particle content. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlators are controlled by an approximate conformal symmetry on the boundary of the spacetime. After classifying all possible contact terms in de Sitter space, we derive an…
We study a cosmological scenario in which inflation is preceded by a bounce. In this scenario, the primordial singularity, one of the major shortcomings of inflation, is replaced by a non-singular bounce, prior to which the universe undergoes a phase of contraction. Our starting point is the bouncing cosmology investigated in Falciano et al. (2008), which we complete by a detailed study of the transfer of cosmological perturbations through the bounce and a discussion of possible observational effects of bouncing cosmologies. We focus on a symmetric bounce and compute the evolution of cosmologi…
A perturbed Reissner-Nordström-de Sitter solution is used to emphasize the nature of the singularity along the Cauchy horizon of a charged spherically symmetric black hole. For these solutions, conditions may prevail under which the mass function is bounded and yet the curvature scalar $R_{αβγδ} R^{αβγδ}$ diverges.
We calculate the power spectrum of vacuum fluctuations of a generic scalar field in a quantum cosmological setting that is manifestly singularity-free. The power spectrum is given in terms of the usual scale invariant spectrum plus scale dependent corrections. These are induced by well-defined quantum fluctuations of de Sitter spacetime, resulting in a modified dispersion relation for the scalar field. The leading correction turns out to be proportional to the ratio of Hubble scale and Planck Mass. The maximal relative change in the spectrum is on the ten percent level and might be observable …
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…
Based on entropy considerations and the arrow of time Penrose argued that the universe must have started in a special initial singularity with vanishing Weyl curvature. This is often interpreted to be at odds with inflation. Here we argue just the opposite, that Penrose's persuasions are in fact consistent with inflation. Using the example of power law inflation, we show that inflation begins with a past null singularity, where Weyl tensor vanishes when the metric is initially exactly conformally flat. This initial state precisely obeys Penrose's conditions. The initial null singularity breaks…
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…
Analytical formulas are presented describing a generic singularity inside the static spherically symmetric black holes in the SU(2) Einstein-Yang-Mills-Higgs theories with triplet or doublet Higgs field. The singularity is spacelike and exhibits a `power-low mass inflation'. Alternatively this asymptotic may be interpreted as a pointlike singularity with a non-vanishing shear in the Kantowski-Sachs anisotropic cosmology.
We consider toy cosmological models in which a classical, homogeneous, spinor field provides a dominant or sub-dominant contribution to the energy-momentum tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a field were to exist, appropriate choices of the spinor self-interaction would generate a rich variety of behaviors, quite different from their widely studied scalar field counterparts. We first discuss solutions that incorporate a stage of cosmic inflation and estimate the primordial spectrum of density perturbations seeded during such a stage. Inflation driven by…
We study the phantom inflation in little rip cosmology, in which the current acceleration is driven by the field with the parameter of state w < -1, but since w tends to -1 asymptotically, the rip singularity occurs only at infinite time. In this scenario, before the rip singularity is arrived, the universe is in an inflationary regime. We numerically calculate the spectrum of primordial perturbation generated during this period and find that the results may be consistent with observations. This implies that if the reheating happens again, the current acceleration might be just a start of phan…
On the basis of a semi-classical analysis of vacuum energy in an expanding spacetime, we describe a non-singular cosmological model in which the vacuum density decays with time, with a concomitant production of matter. During an infinitely long period we have an empty, inflationary universe, with H \approx 1. This primordial era ends in a fast phase transition, during which H and Λdecrease to nearly zero in a few Planck times, with release of a huge amount of radiation. The late-time scenario is similar to the standard model, with the radiation phase followed by a long dust era, which tends as…
In this paper, we investigate the effects of Type IV singularity through $f(T)$ gravity description of inflationary universe, where $T$ denotes the torsion scalar. With the Friedmann equations of the theory, we reconstruct a $f(T)$ model according to a given Hubble rate susceptible to describe the inflationary era near the type IV singularity. Moreover, we calculate the Hubble flow parameters in order to determine the dynamical evolution of the cosmological system. The results show that some of the Hubble flow parameters are small near the Type IV singularity and become singular at Type IV Sin…
We study spherical scalar collapse toward a black hole formation and examine the asymptotic dynamics near the central singularity of the formed black hole. It is found that, in the vicinity of the singularity, due to the strong backreaction of a scalar field on the geometry, the mass function inflates and the Kretschmann scalar grows faster than in the Schwarzschild geometry. In collapse, the Misner-Sharp mass is a locally conserved quantity, not providing information on the black hole mass that is measured at asymptotically flat regions.
A semi-classical analysis of vacuum energy in the expanding spacetime suggests that the cosmological term decays with time, with a concomitant matter production. For early times we find, in Planck units, $Λ\approx H^4$, where H is the Hubble parameter. The corresponding cosmological solution has no initial singularity, existing since an infinite past. During an infinitely long period we have a quasi-de Sitter, inflationary universe, with $H \approx 1$. However, at a given time, the expansion undertakes a phase transition, with H and $Λ$ decreasing to nearly zero in a few Planck times, producin…
In this work we investigate which Loop Quantum Cosmology corrected Gauss-Bonnet $F(\mathcal{G})$ gravity can realize two singular cosmological scenarios, the intermediate inflation and the singular bounce scenarios. The intermediate inflation scenario has a Type III sudden singularity at $t=0$, while the singular bounce has a soft Type IV singularity. By using perturbative techniques, we find the holonomy corrected $F(\mathcal{G})$ gravities that generate at leading order the aforementioned cosmologies and we also argue that the effect of the holonomy corrections is minor to the power spectrum…
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…
The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a)~previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b)~the timelike convergence condition is known …
We study the inner-structure of a charged black-hole which is formed from the gravitational collapse of a self-gravitating charged scalar-field. Starting with a regular spacetime, we follow the evolution through the formation of an apparent horizon, a Cauchy horizon and a final central singularity. We find a null, weak, mass-inflation singularity along the Cauchy horizon, which is a precursor of a strong, spacelike singularity along the $r=0$ hypersurface.
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…
