Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes

Ling, Eric

doi:10.1007/s10714-022-02955-y

Cited by 5 publications

(4 citation statements)

References 41 publications

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“…Therefore, an important mathe-JHEP10(2023)182 matical question is to find examples of spacetimes satisfying the hypotheses of Theorem 5.2, which do not belong to the class of past-asymptotically de Sitter spacetimes. The same question remains in the Milne-like case as well [48].…”

Section: Discussion and Future Directionsmentioning

confidence: 91%

“…Specifically, we will mostly explore spacetimes that are flat past-asymptotically dS and derive conditions on their extendibility. There will be many parallels with the works of [38,[46][47][48][49] on the topic of metric extendibility of Milne-like spacetimes, which are homogeneous and isotropic universes with negative (as opposed to zero here) constant spatial curvature.…”

Section: Jhep10(2023)182mentioning

confidence: 98%

“…We choose to focus on flat spatial sections. The issue of extendibility in negatively curved FLRW spacetimes has been studied quite extensively in [29,38,[46][47][48][49]. With positive spatial curvature, some investigations exist as well [29]; in this context, there are examples of pre-inflationary non-singular bounces [57,58], and the issue of setting up the quantum initial conditions has been tackled in [59].…”

Section: Jhep10(2023)182mentioning

confidence: 99%

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On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

Geshnizjani,

Ling,

Quintin

2023

J. High Energ. Phys.

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Inflationary spacetimes have been argued to be past geodesically incomplete in many situations. However, whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be extended (potentially into another phase of the universe) is generally unknown. Both questions have important physical implications. In this paper, we take a closer look at the geometrical structure of inflationary spacetimes and investigate these very questions. We first classify which past inflationary histories have a scalar curvature singularity and which might be extendible and/or non-singular in homogeneous and isotropic cosmology with flat spatial sections. Then, we derive rigorous extendibility criteria of various regularity classes for quasi-de Sitter spacetimes that evolve from infinite proper time in the past. Finally, we show that beyond homogeneity and isotropy, special continuous extensions respecting the Einstein field equations with a perfect fluid must have the equation of state of a de Sitter universe asymptotically. An interpretation of our results is that past-eternal inflationary scenarios are most likely physically singular, except in situations with very special initial conditions.

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Section: Discussion and Future Directionsmentioning

confidence: 91%

Section: Jhep10(2023)182mentioning

confidence: 98%

Section: Jhep10(2023)182mentioning

confidence: 99%

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On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

Geshnizjani,

Ling,

Quintin

2023

J. High Energ. Phys.

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“…Indeed in the dark energy case p = −ρ the above inequality is satisfied and the universe is accelerating. If this is taken as the correct equation of state near the inception of the universe this means that [8] we have ä > 0 at those early time, meaning that if we go back enough to some t c then ȧ(t c ) = 0, and the scale factor reaches a minimal finite size a c = a(t c ) and thus the singularity is avoided. However, this scenario is not plausible because ordinary matter density is expected to be much higher than dark energy density at those early times making the above accelerating scenario invalid.…”

Section: Implications Of the Flrw Equationsmentioning

confidence: 99%

Hybrid Euclidean-Lorentzian Universe

Yahalom

2024

Preprint

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The limited velocity in a geometry of Lorentzian signature, seem to prevent the universe to reach thermodynamic equilibrium as suggested by the cosmic microwave background. Thus it was suggested that the universe which was initially minuscule has reached a more considerable radius in a short duration by a process known as cosmic inflation. However, to drive such a process have led to the suggestion of an ad-hoc scalar field the inflaton, which has no purpose in nature other than driving the cosmic inflation field and then stopping it once the universe reached the right size. In a recent paper it was shown that rapid expansion can occur without postulating an inflation by following Hawking's suggestion and assuming that primordially the metric of the universe had an Euclidean signature, in which case velocity is not limited and thermalization and rapid expansion are derived without the need to assume an ad-hoc field. However, while in the previous work emphasis was put on the dynamics and physical statistics of the particles in a Euclidean space vs. Lorentzian space in which both spaces were given. No mathematical model was given regarding the development of current Lorentzian space-time from the early Euclidean space-time, and how fundamental problems such as the space-time singularity and the homogeneity of the CMB can be solved in the hybrid Euclidean-Lorentzian picture. This lacuna is to be rectified in the current paper.

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A Lower Semicontinuous Time Separation Function for $$C^0$$ Spacetimes

Ling

2024

Ann. Henri Poincaré

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The time separation function (or Lorentzian distance function) is a fundamental tool used in Lorentzian geometry. For smooth spacetimes it is known to be lower semicontinuous, and, in fact, continuous for globally hyperbolic spacetimes. Moreover, an axiom for Lorentzian length spaces—a synthetic approach to Lorentzian geometry—is the existence of a lower semicontinuous time separation function. Nevertheless, the usual time separation function is not necessarily lower semicontinuous for $$C^0$$ C 0 spacetimes due to bubbling phenomena. In this paper, we introduce a class of curves called “nearly timelike” and show that the time separation function for $$C^0$$ C 0 spacetimes is lower semicontinuous when defined with respect to nearly timelike curves. Moreover, this time separation function agrees with the usual one when the metric is smooth. Lastly, sufficient conditions are found guaranteeing the existence of nearly timelike maximizers between two points in a $$C^0$$ C 0 spacetime.

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Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes

Cited by 5 publications

References 41 publications

On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

Hybrid Euclidean-Lorentzian Universe

A Lower Semicontinuous Time Separation Function for $$C^0$$ Spacetimes

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