Reconstruction of a Scalar-Tensor Theory of Gravity in an Accelerating Universe

Abstract

The present acceleration of the Universe strongly indicated by recent observational data can be modeled in the scope of a scalar-tensor theory of gravity. We show that it is possible to determine the structure of this theory (the scalar field potential and the functional form of the scalar-gravity coupling) along with the present density of dustlike matter from the following two observable cosmological functions: the luminosity distance and the linear density perturbation in the dustlike matter component as functions of redshift. Explicit results are presented in the first order in the small inverse Brans-Dicke parameter ω −1 .PACS numbers: 98.80. Cq, 04.50.+h Recent observational data on type Ia supernovae explosions at high redshifts z ≡ a(t0) a(t) −1 ∼ 1 obtained independently by two groups [1,2], as well as numerous previous arguments (see the recent reviews [3,4]), strongly support the existence of a new kind of matter in the Universe whose energy density not only is positive but also dominates the energy densities of all previously known forms of matter [here a(t) is the scale factor of the FriedmannRobertson-Walker (FRW) isotropic cosmological model, and t 0 is the present time]. This form of matter has a strongly negative pressure and remains unclustered at all scales where gravitational clustering of baryons and (nonbaryonic) cold dark matter (CDM) is seen. Its gravity results in the present acceleration of the expansion of the Universe:ä(t 0 ) > 0. In a first approximation, this kind of matter may be described by a constant Λ-term in the gravity equations as first introduced by Einstein. However, a Λ-term could also be slowly varying with time. If so, this will be soon determined from observational data. In particular, if we use the simplest model of a variable Λ-term (also called quintessence in [5]) borrowed from the inflationary scenario of the early Universe, namely an effective scalar field Φ with some self-interaction potential U (Φ) minimally coupled to gravity, then the functional form of U (Φ) can be determined from observational cosmological functions: either from the luminosity distance D L (z) [6,7], or from the linear density perturbation in the dustlike component of matter in the Universe δ m (z) for a fixed comoving smoothing radius [6]. However, this model cannot account for any future observational data, in particular, for any functional form of D L (z). This happens because a variable Λ-term in this model should satisfy the weak-energy condition ε Λ +p Λ ≥ 0. In terms of the observable quantity H(z) ≡ȧ(t)/a(t) describing the evolution of the expanding Universe at recent epochs, the following inequality should be satisfied [4]Here, H 0 = H(z = 0) is the Hubble constant, Ω m,0 is the present energy density of the dustlike (CDM+baryons) matter component in terms of the critical density ε crit = 3H 2 0 /8πG (c =h = 1, and an index 0 stands for the present value of the corresponding quantity). Note that the inequality (1) saturates when the Λ-term is exactly constant. It is not clear fr...

Oxidised cosmic acceleration

“…These terms are essential in anomaly cancellation, in finding N = 1 string vacua, and in the overall consistency of the theory. If Einstein's equations are modified, it may be easier to violate the NEC without causing pathologies [54,55]. The no-go theorems indicate that, in some circumstances, these NEC-violating mechanisms must play an essential role in accommodating accelerating universes.…”

“…Certainly the NEC forbids a number of solutions to Einstein's equations with strange properties: traversable wormholes [37,38], superluminal "warp drives" [39,40,41,42,43,44], time machines [45,46], universes with big rip singularities [47,48], and pathologies with gravitational thermodynamics [49,50,51,52,53] are possible with NECviolating "exotic" matter. 2 (If one considers non-Einstein gravity, these conclusions may differ: for example, the NEC can be violated by a scalar field in Brans-Dicke gravity in Jordan frame [54] without allowing wormholes [55]). Whether exotic NEC-violating possibilities should be allowed is perhaps a matter of taste.…”

A simplified approach to general scalar-tensor theories

“…In order to obtain a homogeneous and isotropic expansion, the mechanism behind the accelerated expansion is typically attributed to a (effective) scalar field. It is, however, generally straightforward to select parameters for a model to select the desired expansion history of the universe [4][5][6][7][8], and so it is important to investigate the perturbative behavior of a model in order to establish observational limits on the parameter space. Unfortunately, this analysis is typically much harder to perform than the background analysis.…”

Loop quantum modified gravity and its cosmological application

“…Now we can make a second canonical transformation via defining: 16) where Γ i a is the spin connection determined by E a i , and γ is a nonzero real number. It is easy to see that our new variable A j a coincides with the Ashtekar-Barbero connection [28,29] in the special case φ = 1.…”

“…Since it can naturally lead to cosmological acceleration in certain models (see e.g. [16][17][18][19]), the scalar field in STT of gravity is expected to account for the "dark energy" problem. In addition, some models of STT of gravity may even account for the "dark matter" puzzle [20][21][22], which was revealed by the observed rotation curve of galaxy clusters.…”