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A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach de Sitter space. The action for this theory is obtained by a higher derivative modification of Einstein's theory. We expect that our model can easily be generalized to solve the singularity problem also for anisotropic cosmologies.

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“…In this case, equations (3.1) and (3.2) generalize to (see (2.26) and (2.27)) 25) where the constant c is as in Eq. (3.21).…”

Section: Nonsingular Universe Without Limiting Curvaturementioning

confidence: 99%

Cosmological theory without singularities

1993

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“…It is well known, that in many cases the physically important classical solutions are due to higher derivatives (for example, inflation may be achieved in this way [175,127]). …”

Section: What Is the Difference With Metric?mentioning

confidence: 99%

Physical aspects of the space–time torsion

2002

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Abstract. We review many quantum aspects of torsion theory and discuss the possibility of the space-time torsion to exist and to be detected. The paper starts, in Chapter 2, with a pedagogical introduction to the classical gravity with torsion, that includes also interaction of torsion with matter fields. Special attention is paid to the conformal properties of the theory. In Chapter 3, the renormalization of quantum theory of matter fields and related topics, like renormalization group, effective potential and anomalies, are considered. Chapter 4 is devoted to the action of spinning and spinless particles in a space-time with torsion, and to the discussion of possible physical effects generated by the background torsion. In particular, we review the upper bounds for the magnitude of the background torsion which are known from the literature. In Chapter 5, the comprehensive study of the possibility of a theory for the propagating completely antisymmetric torsion field is presented. It is supposed that the propagating field should be quantized, and that its quantum effects must be described by, at least, some effective low-energy quantum field theory. We show, that the propagating torsion may be consistent with the principles of quantum theory only in the case when the torsion mass is much greater than the mass of the heaviest fermion coupled to torsion. Then, universality of the fermion-torsion interaction implies that torsion itself has a huge mass, and can not be observed in realistic experiments. Thus, the theory of quantum matter fields on the classical torsion background can be formulated in a consistent way, while the theory of dynamical torsion meets serious obstacles. In Chapter 6, we briefly discuss the string-induced torsion and the possibility to induce torsion action and torsion itself through the quantum effects of matter fields.

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“…For α 2 > 4 we have further the solution (23), (37) with negative H. Forα 2 < 2 and α 2 > 2 a pure scalar field cosmology therefore describes a Universe where the scale factor a(t) first increases exponentially, and subsequently decreases exponentially. For all times the effective Planck mass χ grows exponentially.…”

Section: Asymptotic Early Cosmologymentioning

confidence: 99%

“…With this scaling and for constant K we find again a de Sitter solution (23), (24), (25), (27), (28). In order to realize eq.…”

Section: Radiation Dominationmentioning

confidence: 99%

“…During the inflationary epoch the energy density of the Universe is dominated by the potential energy of a scalar field, the inflaton, causing a very rapid expansion [22][23][24][25][26][27]. We link this inflationary phase to quintessence in late cosmology, where the scalar field again plays an important role [9,21,[28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

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Variable gravity Universe

2014

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For variable gravity models the strength of gravity, as measured by Newton's "constant" or the Planck mass, depends on the value of a scalar field, the cosmon. We discuss two simple fourparameter models with a quadratic or constant cosmon potential. They are compatible with all presently available cosmological observations, including inflation. The inflaton and the scalar field of quintessence are the same cosmon field. Dark Energy constitutes a small, almost constant fraction of the energy density during the radiation and matter dominated epochs (Early Dark Energy). In the present epoch we witness a transition to a new Dark Energy dominated epoch. Our models are free of a big bang singularity. The stability of solutions generates an arrow of time. Our picture of the Universe is unusual, with a shrinking or static scale factor, while the masses of particles increase and the size of atoms shrinks. The evolution of the universe can be very slow for all cosmological epochs including inflation, with typical time scale 10 10 yr, and in sharp contrast to the usual big bang picture. The map to the equivalent Einstein frame with constant particle masses and expanding scale factor can be singular at the big bang.

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Une leçon de flûte

Cited by 12 publications

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Cosmological theory without singularities

Cosmological theory without singularities

Physical aspects of the space–time torsion

Variable gravity Universe

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