Higher Derivative Scalar Tensor Theory in Unitary Gauge

Abstract

Ostrogradsky instability generally appears in nondegenerate higher-order derivative theories and this issue can be resolved by removing any existing degeneracy present in such theories. We consider an action involving terms that are at most quadratic in second derivatives of the scalar field and nonminimally coupled with the curvature tensors. We perform a 3+1 decomposition of the Lagrangian to separate second-order time derivative terms from rest. This decomposition is useful for checking the degeneracy hidden in the Lagrangian and helps us find conditions under which Ostrogradsky instability does not appear. We show that our construction of Lagrangian resembles that of a GRlike theory for a particular case in the unitary gauge. As an example, we calculate the equation of motion for the flat FRW. We also write the action for open and closed cases, free from higher derivatives for a particular choice derived from imposing degeneracy conditions.

Spatially covariant gravity with nonmetricity

“…Conversely, a SCG theory can be recast as a GST theory by the gauge recovering procedure (Stückelberg trick). Such a correspondence between SCG and GST theories has been discussed in detail in [32][33][34] (see also [35,36]).…”

Power spectra and circular polarization of primordial gravitational waves with parity and Lorentz violations

“…However, possible violations of these two symmetries may arise in theories that try to unify quantum physics with gravity. Because of this, various modified theories of gravity have been proposed to explore the nature of parity and Lorentz violations in gravity, to mention a few, including the Chern-Simons modified gravity [28,29], the symmetric teleparallel equivalence JCAP07(2024)005 of GR theory [30,31], Horava-Lifshitz theories of quantum gravity [32][33][34][35][36][37][38], chiral scalar-tensor theory [39], the Nieh-Yan teleparallel modified gravity [40][41][42], parity-violating scalar-tensor theory in teleparallel gravity [43], parity violation induced by couplings between dual Reimann tensor and Kalb-Ramond two-form field [44], the linearized gravity in standard model extension [45,46], Einstein-AEther theories [47][48][49][50][51][52][53][54], and the spatial covariant gravities [55][56][57][58][59][60], etc.…”

Hamiltonian analysis of nonlocal F(R) gravity models

“…Generally, these instabilities are easy to identify by linear momentum terms within the Hamiltonian, which make it unbounded above and below depending on the structure [25]. However degenerate theories [26][27][28][29][30][31][32][33][34][35](for review, refer to [36,37]) in this regard is free from these instabilities by reducing the phase space non trivially [38] In order to check the appearance of Ostrogradsky instability in any higher derivative theory, a Hamiltonian analysis would be required. The Hamiltonian analysis of these types of theories can be performed by the Dirac method of constraint system [39][40][41][42][43].…”