Canonical formulation of scalar curvature squared action in higher dimensions

Canonical formulation for an action containing scalar curvature squared term $(R^2)$ in arbitrary dimension has been performed in maximally symmetric space-time. The quantum dynamics does not alter significantly from the same in $4$-dimension. Classical solution is also at par with the one presented by Starobinsky. WKB approximation peaks around the classical solution.Comment: 11 pages. To appear in Phys. Rev. D (2014

History of cosmic evolution with modified Gauss-Bonnet-dilatonic coupled term

Gauss-Bonnet-dilatonic coupling in four dimension plays an important role to explain late time cosmic evolution. However, this term is an outcome of low energy string effective action and thus ought to be important in the early universe too. Unfortunately, phase-space formulation of such a theory does not exist in the literature due to branching. We therefore consider a modified theory of gravity, which contains a nonminimally coupled scalar-tensor sector in addition to higher order scalar curvature invariant term with Gauss-Bonnet-dilatonic coupling. Such an action unifies early inflation with late-time cosmic acceleration. Quantum version of the theory is also well-behaved.Comment: 13 pages, 5 figures, To appear in EPJC (2017

Thermodynamics of irreversible particle creation phenomena and its cosmological consequence

The study of particle creation phenomena at the expense of the gravitational field is of great research interest. It might solve the cosmological puzzle single-handedly, without the need for either dark energy or the modified theory of gravity. In the early universe, following graceful exit from inflationary phase, it serves the purpose of reheating the cold universe, which gave way to the hot Big-Bang model. In the late universe, it led to late time cosmic acceleration, without affecting stand-ard Big-Bang-Nucleosynthesis (BBN), Cosmic Microwave Background Radiation (CMBR), or Structure Formation. In this chapter, we briefly review the present status of cosmic evolution, develop the thermodynamics for irreversible particle creation phenomena and study its consequences at the early as well as in the late universe.Comment: 28 pages, 3 figures, To appear in 'CFD Technics and Thermo-Mechanics Applications', Springer, Chapter - N

Canonical formulation of curvature squared action in the presence of lapse function

Lapse function appears as Lagrange multiplier in Einstein-Hilbert action and its variation leads to the (0 0) equation of Einstein, which corresponds to the Hamiltonian constraint equation. In higher order theory of gravity the situation is not that simple. Here, we take up the curvature squared (R^2) action being supplemented by an appropriate boundary term in the background of Robertson-Walker minisuperspace metric, and show how to identify the constraint equation and formulate the Hamiltonian without detailed constraint analysis. The action is finally expressed in the canonical form $A = \int(\dot h_{ij} \pi^{ij} + \dot K_{ij}\Pi^{ij} - N{\mathcal H})dt \sim d^3 x$, where, the lapse function appears as Lagrange multiplier, once again. Canonical quantization yields Schr\"odinger like equation, with nice features. To show that our result is not an artifact of having reduced the theory to a measure zero subset of its configuration space, the role of the lapse function as Lagrangian multiplier has also been investigated in Bianchi-I, Kantowski-Sachs and Bianchi-III minisuperspace metrics. Classical and semiclassical solutions have finally been presented.Comment: 24 pages, no figur

Viability of Noether symmetry of F(R) theory of gravity

Canonization of F(R) theory of gravity to explore Noether symmetry is performed treating R - 6(\frac{\ddot a}{a} + \frac{\dot a^2}{a^2} + \frac{k}{a^2}) = 0 as a constraint of the theory in Robertson-Walker space-time, which implies that R is taken as an auxiliary variable. Although it yields correct field equations, Noether symmetry does not allow linear term in the action, and as such does not produce a viable cosmological model. Here, we show that this technique of exploring Noether symmetry does not allow even a non-linear form of F(R), if the configuration space is enlarged by including a scalar field in addition, or taking anisotropic models into account. Surprisingly enough, it does not reproduce the symmetry that already exists in the literature (A. K. Sanyal, B. Modak, C. Rubano and E. Piedipalumbo, Gen.Relativ.Grav.37, 407 (2005), arXiv:astro-ph/0310610) for scalar tensor theory of gravity in the presence of R^2 term. Thus, R can not be treated as an auxiliary variable and hence Noether symmetry of arbitrary form of F(R) theory of gravity remains obscure. However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar-tensor theory (A. K. Sanyal, Phys.Lett.B624, 81 (2005), arXiv:hep-th/0504021 and Mod.Phys.Lett.A25, 2667 (2010), arXiv:0910.2385 [astro-ph.CO]). Here, we briefly expatiate the non-Noether conserved current and cite an example to reveal its importance in finding cosmological solution for such an action, taking F(R) \propto R^{3/2}.Comment: 16 pages, 1 figure. appears in Int J Theoretical Phys (2012

Canonical equivalence, quantization and inflation for higher-order theory of gravity

Canonical formulation of higher-order theory of gravity has been attempted over decades. Different routes lead to different phase-space structures of the Hamiltonian. Although, these Hamiltonians are canonically equivalent at the classical level, their quantum counterparts may not be same, due to nonlinearity. Earlier, it has been proved that ‘Dirac constraint analysis’ (after taking care of divergent terms) and ‘Modified Horowitz’ Formalism’ lead to identical phase-space structure of the Hamiltonian for the gravitational action with scalar curvature squared terms. For the sake of completeness, this paper expatiates the extension of the same work for a general fourth-order gravitational action. Canonical quantization and semiclassical approximation are performed to explore that such a quantum theory transits successfully to a classical de-Sitter Universe. Inflation is also studied. Inflationary parameters show excellent agreement with the recently released Planck’s data. </jats:p