We provide a novel mechanism that resolves the Big Bang Singularity present in FRW space-times without the need for ghost fields. Building on the fact that a four-fermion interaction arises in General Relativity when fermions are covariantly coupled, we show that at early times the decrease in scale factor enhances the correlation between pairs of fermions. This enhancement leads to a BCS-like condensation of the fermions and opens a gap dynamically driving the Hubble parameter $H$ to zero and results in a non-singular bounce, at least in some special cases.
We present a simplified dynamic-vacuum-energy model for a time-symmetric Milne-like universe. The big bang singularity in this simplified model, like the one in a previous model, is just a coordinate singularity with finite curvature and energy density. We then calculate the dynamic behavior of scalar metric perturbations and find that these perturbations destabilize the big bang singularity.
The origin of Big Bang singularity in 3+1 dimensions can be understood in an exact string theory background obtained by an analytic continuation of a cigar like geometry with a nontrivial dilaton. In a T-dual conformal field theory picture there exists a closed string tachyon potential which excises the singular space-time of a strongly coupled regime to ensure that a higher dimensional universe has no curvature singularity. However in 3+1 dimensions the universe exhibits all the pathology of a standard Big Bang cosmology. The emergence of a singularity now owes to a higher dimensional orbifol…
Following up on earlier work on the regularization of the singular Schwarzschild solution, we now apply the same procedure to the singular Friedmann solution. Specifically, we are able to remove the divergences of the big bang singularity, at the price of introducing a 3-dimensional spacetime defect with a vanishing determinant of the metric. This particular regularization also suggests the existence of a "pre-big-bang" phase.
We propose a picture, within the pre-big-bang approach, in which the universe emerges from a bath of plane gravitational and dilatonic waves. The waves interact gravitationally breaking the exact plane symmetry and lead generically to gravitational collapse resulting in a singularity with the Kasner-like structure. The analytic relations between the Kasner exponents and the initial data are explicitly evaluated and it is shown that pre-big-bang inflation may occur within a dense set of initial data. Finally, we argue that plane waves carry zero gravitational entropy and thus are, from a thermo…
A simple model for a scalar field and gravity admits homogeneous isotropic cosmological solutions which cross the Big Bang singularity. In the scaling frame with field dependent effective Planck mass these solutions are regular. They become singular in the Einstein frame with fixed Planck mass. This field singularity arises since the field transformation of the metric to the Einstein frame is singular at the crossing point of a vanishing scalar field. No physical singularity is present for these solutions. Within general models with no more than two derivatives we find that the possibility of …
In this note, we investigate the possibility of avoiding the Big Bang singularity with a single scalar field which couples non-minimally to gravity. We show that in the case that gravity couples linearly to the field, some severe conditions on the field's potential have to be imposed. However, in non-linear case, it is quite generic to avoid the singularity with single scalar field.
We present a physics model for a time-symmetric Milne-like universe. The model is based on the $q$-theory approach to the cosmological constant problem, supplemented by an assumed vacuum-matter energy exchange possibly due to quantum-dissipative effects. Without fine-tuning of the initial vacuum energy density, we obtain a harmless big bang singularity (with finite values of the Ricci and Kretschmann curvature scalars) and attractor behavior towards Minkowski spacetime. The time-symmetric spacetime manifold of our model may provide the proper setting for a possible CPT-symmetric universe.
We propose a new version of the $AdS/CFT$ correspondence, where polymer structures similar to Loop Quantum Cosmology spin networks can be induced on an isotropic and homogeneous flat Randall-Sundrum II brane, corresponding to the holographic duals of closed string states living in the bulk. Such polymer structures drive a discrete evolution of the braneworld spacetime that leads to the regularization of the Big Bang singularity. The present results show that the $AdS/CFT$ conjecture can be a possible bridge between String theory and Loop Quantum Gravity.
The creation of universes in entangled pairs may avoid the initial singularity and it would have observable consequences in a large macroscopic universe like ours, at least in principle. In this paper we describe the creation of an entangled pair of universes from a double instanton, which avoids the initial singularity, in the case of a homogeneous and isotropic universe with a conformally coupled massless scalar field. The thermodynamical properties of inter-universal entanglement might have observable consequences on the properties of our single universe provided that the thermodynamics of …
The big bang singularity of the expanding-universe Friedmann solution of the Einstein gravitational field equation can be regularized by the introduction of a degenerate metric and a nonzero length scale $b$. The result is a nonsingular bounce of the cosmic scale factor with a contracting prebounce phase and an expanding postbounce phase. The corresponding maximum values of the curvature and the energy density occur at the moment of the bounce and are proportional to powers of $1/b$. This article presents a detailed calculation of the dynamics of such a nonsingular bounce. In addition, a compa…
A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has noncommutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates …
The singularity for the big bang state can be represented using the generalized anisotropic Friedmann equation, resulting in a system of differential equations in a central force field. We study the regularizability of this singularity as a function of a parameter, the equation of state, $w$. We prove that for $w >1$ it is regularizable only for $w$ satisfying relative prime number conditions, and for $w \leq 1$ it can always be regularized. This is done by using a McGehee transformation, usually applied in the three and four-body problems. This transformation blows up the singularity into an …
We elaborate on a recently discovered phenomenon where a scalar field close to big-bang is forced to climb a steep potential by its dynamics. We analyze the phenomenon in more general terms by writing the leading order equations of motion near the singularity. We formulate the conditions for climbing to exist in the case of several scalars and after inclusion of higher-derivative corrections and we apply our results to some models of moduli stabilization. We analyze an example with steep stabilizing potential and notice again a related critical behavior: for a potential steepness above a criti…
We study the classical dynamics of the universe undergoing a transition from contraction to expansion through a big bang singularity. The dynamics is described by a system of differential equations for a set of physical quantities, such as the scale factor $a$, the Hubble parameter $H$, the equation of state parameter $w$, and the density parameter $Ω$. The solutions of the dynamical system have a singularity at the big bang. We study if the solutions can be regularized at the singularity in the sense of whether they have unique branch extensions through the singularity. In particular, we cons…
In the recently proposed cosmological constant (CC) filter mechanism based on modified gravity in the Palatini formalism, gravity in the radiation, matter and late-time de Sitter eras is insensitive to energy sources with the equation of state -1. This implies that finite vacuum energy shifts from phase transitions are filtered out, too. In this work we investigate the CC filter model at very early times. We find that the initial big bang singularity is replaced by a cosmic bounce, where the matter energy density and the curvature are finite. In a certain case this finiteness can be observed a…
Big bang of the Friedmann-Robertson-Walker (FRW)-brane universe is studied. In contrast to the spacelike initial singularity of the usual FRW universe, the initial singularity of the FRW-brane universe is point-like from the viewpoint of causality including gravitational waves propagating in the bulk. Existence of null singularities (seam singuralities) is also shown in the flat and open FRW-brane universe models.
We analyze the quantum dynamics of the Friedmann-Robertson-Walker Universe in the context of a Generalized Uncertainty Principle. Since the isotropic Universe dynamics resembles that of a one-dimensional particle, we quantize it with the commutation relations associated to an extended formulation of the Heisenberg algebra. The evolution of the system is described in terms of a massless scalar field taken as a relational time. We construct suitable wave packets and analyze their dynamics from a quasi-classical region to the initial singularity. The appearance of a non singular dynamics comes ou…
We study the conformal structure of exotic (non-big-bang) singularity universes using the hybrid big-bang/exotic singularity/big-bang and big-rip/exotic singularity/big-rip models by investigating their appropriate Penrose diagrams. We show that the diagrams have the standard structure for the big-bang and big-rip and that exotic singularities appear just as the constant time hypersurfaces for the time of a singularity and because of their geodesic completeness are potentially transversable. We also comment on some applications and extensions of the Penrose diagram method in studying exotic si…
Despite impressive phenomenological successes, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Depending on the model, one would like to understand how appropriate initial conditions were selected at the big bang singularity, or how a pre-existing contracting universe underwent a big crunch/big bang transition, if such transitions are possible at all. In this talk, after an introduction to these questions, an attempt is described to study cosmological singularities using the AdS/CFT correspondence. A specific model in which asymptotical…
One of the simplest time-dependent solutions of M theory consists of nine-dimensional Euclidean space times 1+1-dimensional compactified Milne space-time. With a further modding out by Z_2, the space-time represents two orbifold planes which collide and re-emerge, a process proposed as an explanation of the hot big bang. When the two planes are near, the light states of the theory consist of winding M2-branes, describing fundamental strings in a particular ten-dimensional background. They suffer no blue-shift as the M theory dimension collapses, and their equations of motion are regular across…
There are no reasons why the singularity in the growth of the dilaton coupling should not be regularised, in a string cosmological context, by the presence of classical inhomogeneities. We discuss a class of inhomogeneous dilaton-driven models whose curvature invariants are all bounded and regular in time and space. We prove that the non-space-like geodesics of these models are all complete in the sense that none of them reaches infinity for a finite value of the affine parameter. We conclude that our examples represent truly singularity-free solutions of the low energy beta functions. We disc…
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 …
We consider a contracting universe and its transition to expansion through the big bang singularity with a time varying equation of state $w$, where $w$ approaches $1$ as the universe contracts to the big bang. We show that this singularity is non-regularizable. That is, there is no unique extension of the physical quantities after the transition, but rather infinitely many. This is entirely different from the case of $w > 1$ studied in \cite{Xue:2014}, where $w$ approaches a constant value $w_c > 1$ as the universe contracts. In that case a continuous transition through the big bang to yield …
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…
When quantum gravity is used to discuss the big bang singularity, the most important, though rarely addressed, question is what role genuine quantum degrees of freedom play. Here, complete effective equations are derived for isotropic models with an interacting scalar to all orders in the expansions involved. The resulting coupling terms show that quantum fluctuations do not affect the bounce much. Quantum correlations, however, do have an important role and could even eliminate the bounce. How quantum gravity regularizes the big bang depends crucially on properties of the quantum state.
We study a quantum Hot Big Bang in the connection representation, with a matter constant of motion m whose conjugate defines time. Superpositions in m induce a unitary inner product. The wavefunction reveals a resolution of the singularity problem without new physics or supplementary boundary conditions. Backtracking in time, the probability peak eventually halts at a maximum curvature, its height dropping thereafter while a symmetric contracting peak rises. The Big Bang is replaced by a superposition of contracting and expanding regular Universes. We contrast these findings with the situation…
We discuss how the perturbative particle paradigm fails in certain background with space-like singularity but asymptotically flat which should admit a S-matrix. The Feynman approach relies on the interaction picture. This approach means that we can interpret interactions as exchanges of particles. Particles are the modes of the quadratic part of the Lagrangian. In certain backgrounds with space-like singularity the interaction Hamiltonian is well defined but the perturbative expansion of the evolution operator through the singularity and the perturbative $S$ matrix do not exist. On the other h…
We present classical and quantum dynamics of a test particle in the compactified Milne space. Background spacetime includes one compact space dimension undergoing contraction to a point followed by expansion. Quantization consists in finding a self-adjoint representation of the algebra of particle observables. Our model offers some insight into the nature of the cosmic singularity.
Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and $w-$singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.
We study Big Crunch/Big Bang cosmologies that correspond to exact world-sheet superconformal field theories of type II strings. The string theory spacetime contains a Big Crunch and a Big Bang cosmology, as well as additional ``whisker'' asymptotic and intermediate regions. Within the context of free string theory, we compute, unambiguously, the scalar fluctuation spectrum in all regions of spacetime. Generically, the Big Crunch fluctuation spectrum is altered while passing through the bounce singularity. The change in the spectrum is characterized by a function $Δ$, which is momentum and time…
The light-like linear dilaton background represents a particularly simple time-dependent 1/2 BPS solution of critical type IIA superstring theory in ten dimensions. Its lift to M-theory, as well as its Einstein frame metric, are singular in the sense that the geometry is geodesically incomplete and the Riemann tensor diverges along a light-like subspace of codimension one. We study this background as a model for a big bang type singularity in string theory/M-theory. We construct the dual Matrix theory description in terms of a (1+1)-d supersymmetric Yang-Mills theory on a time-dependent world-…
We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantisation to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t=0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat sp…
Quantum gravity has matured over the last decade to a theory which can tell in a precise and explicit way how cosmological singularities of general relativity are removed. A branch of the universe "before" the classical big bang is obtained which is connected to ours by quantum evolution through a region around the singularity where the classical space-time dissolves. We discuss the basic mechanism as well as applications ranging to new phenomenological scenarios of the early universe expansion, such as an inflationary period.
While most of the singularities of General Relativity are expected to be safely hidden behind event horizons by the cosmic censorship conjecture, we happen to live in the causal future of the classical big bang singularity, whose resolution constitutes the active field of early universe cosmology. Could the big bang be also hidden behind a causal horizon, making us immune to the decadent impacts of a naked singularity? We describe a braneworld description of cosmology with both 4d induced and 5d bulk gravity (otherwise known as Dvali-Gabadadze-Porati, or DGP model), which exhibits this feature…
We analyse numerically the onset of pre-big bang inflation in an inhomogeneous, spherically symmetric Universe. Adding a small dilatonic perturbation to a trivial (Milne) background, we find that suitable regions of space undergo dilaton-driven inflation and quickly become spatially flat ($Ω\to 1$). Numerical calculations are pushed close enough to the big bang singularity to allow cross checks against previously proposed analytic asymptotic solutions.
We present a well-tempered DeWitt wave function, which vanishes at the classical big-bang singularity, in Hořava-Lifshitz (HL) cosmology with tensor perturbation, both analytically and numerically. In general relativity, the DeWitt wave function is ill-behaved once the tensor perturbation is taken into account. This is essentially because the amplitude of the perturbation diverges at the singularity and the perturbative expansion completely breaks down. On the other hand, in HL gravity it is known that the higher dimensional operators required by the perturbative renormalizability render the t…
We study a quotient Conformal Field Theory, which describes a 3+1 dimensional cosmological spacetime. Part of this spacetime is the Nappi-Witten (NW) universe, which starts at a ``big bang'' singularity, expands and then contracts to a ``big crunch'' singularity at a finite time. The gauged WZW model contains a number of copies of the NW spacetime, with each copy connected to the preceeding one and to the next one at the respective big bang/big crunch singularities. The sequence of NW spacetimes is further connected at the singularities to a series of non-compact static regions with closed tim…
Some long standing issues concerning the quantum nature of the big bang are resolved in the context of homogeneous isotropic models with a scalar field. Specifically, the known results on the resolution of the big bang singularity in loop quantum cosmology are significantly extended as follows: i) the scalar field is shown to serve as an internal clock, thereby providing a detailed realization of the `emergent time' idea; ii) the physical Hilbert space, Dirac observables and semi-classical states are constructed rigorously; iii) the Hamiltonian constraint is solved numerically to show that the…
The AdS/CFT correspondence is used to describe five-dimensional cosmology with a big crunch singularity in terms of super-Yang-Mills theory on R times S^3 deformed by a potential which is unbounded below. Classically, a Higgs field in the dual theory rolls to infinity in finite time. But since the S^3 is finite, the unstable mode spreads quantum mechanically and the singularity is resolved when self-adjoint boundary conditions are imposed at infinity. Asymptotic freedom of the coupling governing the instability gives us computational control and the quantum spreading provides a UV cutoff on pa…
We consider branes $N=I\times\so$, where $\so$ is an $n$\ndash dimensional space form, not necessarily compact, in a Schwarzschild-AdS_{(n+2)} bulk $\mc N$. The branes have a big crunch singularity. If a brane is an ARW space, then, under certain conditions, there exists a smooth natural transition flow through the singularity to a reflected brane $\hat N$, which has a big bang singularity and which can be viewed as a brane in a reflected Schwarzschild-AdS_{(n+2)} bulk $\hat{\mc N}$. The joint branes $N\uu \hat N$ can thus be naturally embedded in $R^2\times \so$, hence there exists a second p…
We present a short introduction to a non-standard cosmological scenario motivated by the duality symmetries of string theory, in which the big bang singularity is replaced with a "big bounce" at high but finite curvature. The bouncing epoch is prepared by a long (possibly infinitely extended) phase of cosmic evolution, starting from an initial state asymptotically approaching the string perturbative vacuum.
We construct a new class of 1/4-BPS time dependent domain-wall solutions with null-like metric and dilaton in type II supergravities, which admit a null-like big bang singularity. Based on the domain-wall/QFT correspondence, these solutions are dual to 1/4-supersymmetric quantum field theories living on a boundary cosmological background with time dependent coupling constant and UV cutoff. In particular we evaluate the holographic $c$ function for the 2-dimensional dual field theory living on the corresponding null-like cosmology. We find that this $c$ function runs in accordance with the $c$-…
Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS_3-gravity can be written as an SL(2,C) Chern-Simons theory, we investigate SL(3,C) Chern-Simons theory as a higher-spin context in which these singularities might get resolved. As in the case of higher spin black holes in AdS_3, the solutions are invariantly characterized by their holonomies. We show that the dS_3 quotient singularity can be de-singularized by an SL(3,C) gauge transformation tha…
After a brief review of current scenarios for the resolution and/or avoidance of the Big Bang, an alternative hypothesis is put forward implying an infinite increase in complexity towards the initial singularity. This may result in an effective non-calculability which would present an obstruction to actually reaching the beginning of time. This proposal is motivated by the appearance of certain infinite-dimensional duality symmetries of indefinite Kac--Moody type in attempts to unify gravity with the fundamental matter interactions, and deeply rooted in properties of Einstein's theory.
We consider spacetimes $N$ satisfying some structural conditions, which are still fairly general, and prove convergence results for the leaves of an inverse mean curvature flow. Moreover, we define a new spacetime $\hat N$ by switching the light cone and using reflection to define a new time function, such that the two spacetimes $N$ and $\hat N$ can be pasted together to yield a smooth manifold having a metric singularity, which, when viewed from the region $N$ is a big crunch, and when viewed from $\hat N$ is a big bang. The inverse mean curvature flows in $N$ \resp $\hat N$ correspond to ea…
Central European Institute for Cosmology and Fundamental Physics (CEICO), Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所中欧宇宙学与基础物理研究所）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（东京大学大学院理学研究系早期宇宙研究中心）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo（东京大学前沿研究机构宇宙物理与数学卡弗里研究所）；Institut d’Astrophysique de Paris, UMR-7095 du CNRS（巴黎天体物理研究所法国国家科学研究中心联合研究实验室）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
We propose a gravitational model with a Brans-Dicke-type scalar field having, in the would-be action, a "wrong-sign" kinetic term and a quartic interaction term. In a cosmological context, we obtain, depending on the boundary conditions, either the Friedmann solution or a kink-bounce solution. The expanding-universe Friedmann solution has a big bang curvature singularity, whereas the kink-bounce solution has a nonsingular bouncing behavior of the cosmic scale factor. The bounce occurs precisely at the moment when the scalar field of the kink-type configuration goes through zero, making for a v…
Energy Momentum Squared Gravity (EMSG) is a cosmological model where the scale factor is non vanishing at all times and hence does not favor big bang cosmology. However, the profile of density in the radiation dominated universe shows that EMSG supports inflationary cosmology. Inflationary cosmological models are successful in providing convincing answers to major cosmological issues like horizon problem, flatness problem and small value of cosmological constant but hitherto no model of inflation has been observationally confirmed. Owing to this, Varying Speed of Light (VSL) were introduced wh…
We completely classify Friedmann-Lemaître-Robertson-Walker solutions with spatial curvature $K=0,\pm 1$ and equation of state $p=wρ$, according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditions and allow $ρ< 0$, thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for $w>-1/3$ and $ρ>0$, while no big-bang singularity for $w<-1$ and $ρ>0$. For $K=0$ or $-1$, $-1<w<-1/3$ and $ρ>0$, there is an initial null big-bang singularity. For each spatial curvature, there i…
We confront the big bang for the beginning of the universe with an equivalent picture of a slow freeze - a very cold and slowly evolving universe. In the freeze picture the masses of elementary particles increase and the gravitational constant decreases with cosmic time, while the Newtonian attraction remains unchanged. The freeze and big bang pictures both describe the same observations or physical reality. We present a simple "crossover model" without a big bang singularity. In the infinite past space-time is flat. Our model is compatible with present observations, describing the generation …
Alternative scenarios to the Big Bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal cosmological volume or by some early quantum phase. This latter scenario was devised a long time ago and referred as an "emergent universe" (in the sense that our universe emerged from a constant volume quantum phase). We show here that within an improved framework of canonical quantum gravity (the so called Quantum Reduced Loop Gravity) the Friedmann equations for co…
Important open questions in cosmology require a better understanding of the Big Bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like Big Bang models, presenting both solved and open problems.
Massive gravity is a modified theory of general relativity. In this paper, we study, using a method in which the scale factor changes as a particle in a "potential", all possible cosmic evolutions in a ghost-free massive gravity. We find that there exists, in certain circumstances, an oscillating universe or a bouncing one. If the universe starts at the oscillating region, it may undergo a number of oscillations before it quantum mechanically tunnels to the bounce point and then expand forever. But going back to the singularity from the oscillating region is physically not allowed. So, the big…
