Higher Derivative Theory for Curvature Term Coupling with Scalar Field

Joshi, Pawan; Panda, Sukanta

doi:10.1007/978-981-33-4408-2_128

Cited by 4 publications

(3 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(3.8), the LSDS and LSDM are the only existing problematic terms in the L 1−6 with the Lagrangian coefficient D 1 . In order to remove LSDS and LSDM, the only option is the D 1 = 0 [55], a trivial choice. This theory can also be checked in the unitary gauge to eliminate problematic terms, but there are no other options besides a trivial one.…”

Section: Ghost Free Lagrangian In Unitary Gaugementioning

confidence: 99%

Ghost free theory in unitary gauge: a new candidate

Joshi

Panda

Vidyarthi

2023

J. Cosmol. Astropart. Phys.

Self Cite

View full text Add to dashboard Cite

We propose an algebraic analysis using a 3+1 decomposition to identify conditions for a clever cancellation of the higher derivatives, which plagued the theory with Ostrogradsky ghosts, by exploiting some existing degeneracy in the Lagrangian. We obtain these conditions as linear equations (in terms of coefficients of the higher derivative terms) and demand that they vanish, such that the existence of nontrivial solutions implies that the theory is degenerate. We find that, for the theory under consideration, no such solutions exist for a general inhomogeneous scalar field, but that the theory is degenerate in the unitary gauge. We, then, find modified FLRW equations and narrow down conditions for which there could exist a de Sitter inflationary epoch. We further find constraints on the coefficients of the remaining higher-derivative interaction terms, based on power-counting renormalizability and tree-level unitarity up to the Planck scale.

show abstract

Section: Ghost Free Lagrangian In Unitary Gaugementioning

confidence: 99%

Ghost free theory in unitary gauge: a new candidate

Joshi

Panda

Vidyarthi

2023

J. Cosmol. Astropart. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is already mentioned earlier that Cµνρσ contains only the linear curvature coupling terms, so its possible structure is given by [66],…”

Section: Construction Of Cµνρσmentioning

confidence: 99%

Higher derivative scalar tensor theory in unitary gauge

Joshi

Panda

2022

J. Cosmol. Astropart. Phys.

Self Cite

View full text Add to dashboard Cite

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 non-minimally 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 GR-like 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.

show abstract

“…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 [20]. However degenerate theories [21][22][23][24][25][26][27][28][29][30](for review, refer to [31,32]) in this regard is free from these instabilities by reducing the phase space non trivially [33] 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 [34][35][36][37][38].…”

mentioning

confidence: 99%

Hamiltonian Analysis of Nonlocal F(R) Gravity Models

Joshi,

Panda

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We construct a Hamiltonian for the nonlocal F(R) theory in the present work. By this construction, we demonstrate the nature of the ghost degrees of freedom. Finally, we find conditions that give rise to ghost-free theories. I. INTRODUCTIONThe theoretical explanation of the ongoing accelerated expansion of the universe[1-6] is one of the most unsolved cosmological problems. Achieving accelerated expansion by adding a constant to Einstein-Hilbert(E-H) action suffers from fine-tuning problem [7]. There are many ways to explain the accelerated epoch of the current universe. In this context modified gravity theories have been developed by modifying the E-H action, for example, F(R) theories of gravity [8][9][10][11][12][13]. In recent times another class of most popular modified gravity theories is nonlocal gravity models [14,15]. These models are motivated by Einstein action's ultraviolet (UV) and infrared (IR) corrections. They also provide a theoretical explanation of the accelerated expansion of the current universe. Some salient features of nonlocal gravity models are: (1) they can be employed to study cosmology in both the infrared and the ultraviolet, (2) valid cosmological perturbation theory, and (3) the resulting cosmology has good agreement with most observations. In this direction, the nonlocal terms with Ricci scalar R and F (R) are extensively studied along with Einstein Hilbert action. These terms involve analytic transcendental functions of the covariant d'Alembert operator . Initially, as developed by Wetterich, models with correction terms like R −1 R are shown to be effective IR corrected nonlocal gravity model [16]. Further, Deser and Woodard[17] introduce a general form asRf ( 1 R) which can be responsible for the late-time cosmic expansion of the universe. In this line, for a recent review on this topic, refer to [18].The nonlocal theory can have an equivalent scalar-tensor form by introducing auxiliary variables. Higher derivative terms with d'Alembertian operator and curvature can be considered higher derivative field theories. According to Ostrogradsky theorem[19], non-degenerate higher derivative Lagrangians are cursed with instabilities (popularly known Ostrogradsky instabilities). 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 [20]. However degenerate theories [21][22][23][24][25][26][27][28][29][30](for review, refer to [31,32]) in this regard is free from these instabilities by reducing the phase space non trivially [33] 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 [34][35][36][37][38]. The Hamiltonian analysis of the nonlocal model with inverse powers of d'Alembertian operators acting only on Ricci scalar is performed in [39]. A more general analysis of constructing Hami...

show abstract

Higher Derivative Theory for Curvature Term Coupling with Scalar Field

Cited by 4 publications

References 6 publications

Ghost free theory in unitary gauge: a new candidate

Ghost free theory in unitary gauge: a new candidate

Higher derivative scalar tensor theory in unitary gauge

Hamiltonian Analysis of Nonlocal F(R) Gravity Models

Contact Info

Product

Resources

About