scholarly journals The atoms of space, gravity and the cosmological constant

2016 ◽  
Vol 25 (07) ◽  
pp. 1630020 ◽  
Author(s):  
T. Padmanabhan
Keyword(s):  
Cosmological Constant ◽  
Density Of States ◽  
Zero Point ◽  
Integration Constant ◽  
Quantum Structure ◽  
Field Equations ◽  
Classical Gravity ◽  
Matter Sector ◽  
Null Surfaces

I describe an approach which connects classical gravity with the quantum microstructure of spacetime. The field equations arise from maximizing the density of states of matter plus geometry. The former is identified using the thermodynamics of null surfaces while the latter arises due to the existence of a zero-point length in the spacetime. The resulting field equations remain invariant when a constant is added to the matter Lagrangian, which is a symmetry of the matter sector. Therefore, the cosmological constant arises as an integration constant. A nonzero value [Formula: see text] of the cosmological constant renders the amount of cosmic information [Formula: see text] accessible to an eternal observer finite and hence is directly related to it. This relation allows us to determine the numerical value of [Formula: see text] from the quantum structure of spacetime.

scholarly journals Cosmological constant from the emergent gravity perspective

2014 ◽  
Vol 23 (06) ◽  
pp. 1430011 ◽  
Author(s):  
T. Padmanabhan ◽  
Hamsa Padmanabhan
Keyword(s):  
Cosmological Constant ◽  
Sufficient Conditions ◽  
Integration Constant ◽  
Dimensionless Number ◽  
Late Time ◽  
Field Equations ◽  
Cosmological Constant Problem ◽  
Emergent Gravity ◽  
Background Material ◽  
The Universe

Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant Λ, with the dimensionless parameter [Formula: see text], where LP= (Għ/c3)1/2is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally satisfied in the emergent gravity paradigm in which (i) the field equations of gravity are invariant under the addition of a constant to the matter Lagrangian and (ii) the cosmological constant appears as an integration constant in the solution. The numerical value of this integration constant can be related to another dimensionless number (called CosMIn) that counts the number of modes inside a Hubble volume that cross the Hubble radius during the radiation and the matter-dominated epochs of the universe. The emergent gravity paradigm suggests that CosMIn has the numerical value 4π, which, in turn, leads to the correct, observed value of the cosmological constant. Further, the emergent gravity paradigm provides an alternative perspective on cosmology and interprets the expansion of the universe itself as a quest towards holographic equipartition. We discuss the implications of this novel and alternate description of cosmology.

scholarly journals On singular generalized Berwald spacetimes and the equivalence principle

2017 ◽  
Vol 14 (06) ◽  
pp. 1750091 ◽  
Author(s):  
Ricardo Gallego Torromé
Keyword(s):  
Cosmological Constant ◽  
Equivalence Principle ◽  
Physical Significance ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Finsler Spacetime ◽  
Classical Gravity ◽  
Different Levels

The notion of singular generalized Finsler spacetime and singular generalized Berwald spacetime is introduced and their relevance for the description of classical gravity is discussed. A method to construct examples of such generalized Berwald spacetimes is sketched. The method is applied at two different levels of generality. First, a class of flat, singular generalized Berwald spacetimes is obtained. Then in an attempt of further generalization, a class of non-flat generalized Berwald spacetimes is presented and the associated Einstein field equations are discussed. In this context, an argument in favor of a small value of the cosmological constant is given. The physical significance of the models is briefly discussed in the last section.

scholarly journals A Theoretical Calculation of the Cosmological Constant Based on a Mechanical Model of Vacuum

2021 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
Cosmological Constant ◽  
Mass Density ◽  
Zero Point ◽  
Momentum Tensor ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Cosmological Constant Problem ◽  
Metric Tensor ◽  
Point Energy ◽  
Einstein's Equations

We suppose that vacuum is filled with a kind of continuously distributed matter, which may be called the $\Omega(1)$ substratum, or the electromagnetic aether. Lord Kelvin believes that the electromagnetic aether must also generate gravity. We also suppose that vacuum is filled with another kind of continuously distributed substance, which may be called the $\Omega(2)$ substratum. Based on a theorem of V. Fock on the mass tensor of a fluid, the contravariant energy-momentum tensors of the $\Omega(1)$ and $\Omega(2)$ substratums are established. Quasi-static solutions of the gravitational field equations in vacuum are obtained. Based on an assumption, relationships between the contravariant energy-momentum tensor of the $\Omega(1)$ and $\Omega(2)$ substratums and the contravariant metric tensor are obtained. Thus, the cosmological constant is calculated theoretically. The $\Omega(1)$ and $\Omega(2)$ substratums may be a possible candidate of the dark energy. The zero-point energy of electromagnetic fields will not appear as a source term in the Einstein's equations. The cosmological constant problem is one of the puzzles in physics. Some people believed that all kinds of energies should appear as source terms in the Einstein's equations. It may be this belief that leads to the cosmological constant problem. The mass density of the $\Omega(1)$ and $\Omega(2)$ substratums is equivalent to that $31.33195$ protons contained in a box with a volume of $1.0 {m}^{3}$.

scholarly journals Geodesic distance: A descriptor of geometry and correlator of pregeometric density of spacetime events

2020 ◽  
Vol 35 (12) ◽  
pp. 2030008
Author(s):  
T. Padmanabhan
Keyword(s):  
Quantum Theory ◽  
Geodesic Distance ◽  
Zero Point ◽  
Special Role ◽  
Quantum Structure ◽  
Metric Tensor ◽  
Variable Formula ◽  
Classical Geometry ◽  
Tensor Formula ◽  
Null Surfaces

Classical geometry can be described either in terms of a metric tensor [Formula: see text] or in terms of the geodesic distance [Formula: see text]. Recent work, however, has shown that the geodesic distance is better suited to describe the quantum structure of spacetime. This is because one can incorporate some of the key quantum effects by replacing [Formula: see text] by another function [Formula: see text] such that [Formula: see text] is nonzero. This allows one to introduce a zero-point-length in the spacetime. I show that the geodesic distance can be an emergent construct, arising in the form of a correlator [Formula: see text], of a pregeometric variable [Formula: see text], which can be interpreted as the quantum density of spacetime events. This approach also shows why null surfaces play a special role in the interface of quantum theory and gravity. I describe several technical and conceptual aspects of this construction and discuss some of its implications.

scholarly journals WHY DOES GRAVITY IGNORE THE VACUUM ENERGY?

2006 ◽  
Vol 15 (12) ◽  
pp. 2029-2058 ◽  
Author(s):  
T. PADMANABHAN
Keyword(s):  
Gravitational Field ◽  
Cosmological Constant ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Integration Constant ◽  
Field Equations ◽  
Physical Context ◽  
Gravitational Field Equations ◽  
Higher Order Corrections

The equations of motion for matter fields are invariant under the shift of the matter Lagrangian by a constant. Such a shift changes the energy–momentum tensor of matter by [Formula: see text]. In the conventional approach, gravity breaks this symmetry and the gravitational field equations are not invariant under such a shift of the energy–momentum tensor. We argue that until this symmetry is restored, one cannot obtain a satisfactory solution to the cosmological constant problem. We describe an alternative perspective to gravity in which the gravitational field equations are [Gab - κTab]nanb = 0 for all null vectors na. This is obviously invariant under the change [Formula: see text] and restores the symmetry under shifting the matter Lagrangian by a constant. These equations are equivalent to Gab = κTab + Cgab, where C is now an integration constant so that the role of the cosmological constant is very different in this approach. The cosmological constant now arises as an integration constant, somewhat like the mass M in the Schwarzschild metric, the value of which can be chosen depending on the physical context. These equations can be obtained from a variational principle which uses the null surfaces of space–time as local Rindler horizons and can be given a thermodynamic interpretation. This approach turns out to be quite general and can encompass even the higher order corrections to Einstein's gravity and suggests a principle to determine the form of these corrections in a systematic manner.

scholarly journals A Theoretical Calculation of the Cosmological Constant Based on the Theory of Vacuum Mechanics

2019 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
Cosmological Constant ◽  
Energy Momentum Tensor ◽  
Mass Density ◽  
Zero Point ◽  
Momentum Tensor ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Point Energy ◽  
Einstein's Equations

Lord Kelvin believes that the electromagnetic aether must also generate gravity. Based on a theorem of V. Fock on the mass tensor of an elastic continuum, the contravariant energy-momentum tensor of the $\Omega(1)$ substratum is established. Quasi-static solutions of the gravitational field equations in vacuum are obtained. Based on an assumption, relationships between the contravariant energy-momentum tensor of the $\Omega(1)$ substratum and the contravariant metric tensor are obtained. Thus, the cosmological constant is derived theoretically. The $\Omega(1)$ substratum, or we say the electromagnetic aether, may be a possible candidate of the dark energy. The zero-point energy of electromagnetic fields will not appear as a source term in the generalized Einstein's equations. Some people believed that all kinds of energies should appear as source terms in the Einstein's equations. It may be this belief that leads to the so called cosmological constant problem. The mass density of the electromagnetic aether is equivalent to that $31.33195$ protons contained in a box with a volume of $1.0{m}^{3}$.

Cosmological constant Λ in f(R,T) modified gravity

2016 ◽  
Vol 13 (05) ◽  
pp. 1650058 ◽  
Author(s):  
Gyan Prakash Singh ◽  
Binaya Kumar Bishi ◽  
Pradyumn Kumar Sahoo
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Modified Gravity ◽  
Bianchi Type ◽  
Field Equations ◽  
Type Iii ◽  
Expansion Scalar ◽  
Modified Theory Of Gravity ◽  
Shear Scalar ◽  
Modified Theory

In this paper, we have studied the Bianchi type-III cosmological model in the presence of cosmological constant in the context of [Formula: see text] modified theory of gravity. Here, we have discussed two classes of [Formula: see text] gravity, i.e. [Formula: see text] and [Formula: see text]. In both classes, the modified field equations are solved by the relation expansion scalar [Formula: see text] that is proportional to shear scalar [Formula: see text] which gives [Formula: see text], where [Formula: see text] and [Formula: see text] are metric potentials. Also we have discussed some physical and kinematical properties of the models.

scholarly journals TRAVERSABLE WORMHOLES IN (2+1) AND (3+1) DIMENSIONS WITH A COSMOLOGICAL CONSTANT

1995 ◽  
Vol 04 (02) ◽  
pp. 231-245 ◽  
Author(s):  
M.S.R. DELGATY ◽  
R.B. MANN
Keyword(s):  
Energy Density ◽  
Cosmological Constant ◽  
Positive Energy ◽  
Mass Energy ◽  
Field Equations ◽  
Dimensional Solution ◽  
Partial Stability ◽  
Traversable Wormholes ◽  
Spacetime Curvature ◽  
Radial Tension

Macroscopic traversable wormhole solutions to Einstein’s field equations in (2+1) and (3+1) dimensions with a cosmological constant are investigated. Ensuring traversability severely constrains the material used to generate the wormhole’s spacetime curvature. Although the presence of a cosmological constant modifies to some extent the type of matter permitted [for example it is possible to have a positive energy density for the material threading the throat of the wormhole in (2+1) dimensions], the material must still be “exotic,” that is matter with a larger radial tension than total mass-energy density multiplied by c2. Two specific solutions are applied to the general cases and a partial stability analysis of a (2+1) dimensional solution is explored.

scholarly journals The Large Number Hypothesis and Einstein's Theory of Gravitation

1985 ◽  
Vol 38 (4) ◽  
pp. 547 ◽  
Author(s):  
Yun-Kau Lau
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Matter Density ◽  
Time Dependent ◽  
Field Equations ◽  
Large Number Hypothesis ◽  
Theory Of Gravitation ◽  
The Mean ◽  
Limiting Case ◽  
The Universe

In an attempt to reconcile the large number hypothesis (LNH) with Einstein's theory of gravitation, a tentative generalization of Einstein's field equations with time-dependent cosmological and gravitational constants is proposed. A cosmological model consistent with the LNH is deduced. The coupling formula of the cosmological constant with matter is found, and as a consequence, the time-dependent formulae of the cosmological constant and the mean matter density of the Universe at the present epoch are then found. Einstein's theory of gravitation, whether with a zero or nonzero cosmological constant, becomes a limiting case of the new generalized field equations after the early epoch.

scholarly journals Dark Energy as a Cosmological Consequence of Existence of the Dirac Scalar Field in Nature

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
O. V. Babourova ◽  
B. N. Frolov
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Early Universe ◽  
Large Time ◽  
Field Equations ◽  
Conformal Theory ◽  
Effective Cosmological Constant ◽  
Theory Of Gravitation ◽  
Cosmological Consequence

The solution of the field equations of the conformal theory of gravitation with Dirac scalar field in Cartan-Weyl spacetime at the very early Universe is obtained. In this theory dark energy (described by an effective cosmological constant) is a function of the Dirac scalar field β. This solution describes the exponential decreasing of β at the inflation stage and has a limit to a constant value of the dark energy at large time. This can give a way to solving the fundamental cosmological constant problem as a consequence of the fields dynamics in the early Universe.

Sign in / Sign up

Export Citation Format

Share Document