Spacetime as a Complex Network and the Cosmological Constant Problem

Round 1

Reviewer 1 Report

Comments for author File: Comments.pdf

Author Response

Referee comments. Little bit explanation about how a Hamiltonian path/graph can be connected in establishment of partition function may be increases the weight of the section-1. 

Our response. We added the corresponding explanation in Section 1 of the revised manuscript.

Referee comments.  Author has taken Einstein equations for explaining the cosmological constant problem but instead of taking it is better to take any modified theory.

Our response. The cosmological constant problem follows directly from the Einstein equations. According to the equivalence principle, quantum vacuum fluctuations should contribute to the energy-stress tensor and change the magnitude of the cosmological constant. We agree that the solution to this problem is out of the scope of classical general relativity and probably, needs some modification of the theory or another fresh approach. Our paper suggests a solution to this problem based on nonassociative geometry and complex networks.

We are thankful to the referee for the valuable remarks and suggestions.

Reviewer 2 Report

Author proposed a self-tuning solution to the cosmological problem. This approach will definitely motivate other researchers to study other aspects in this area.    

  

Author Response

We are thankful to the referee for the helpful remarks and suggestions.

Reviewer 3 Report

The author creates a potential non-associative geometry and a complex network-based discrete spacetime model. Their method views space as an n-dimensional simplicial 3-complex (or complex network) made up of entangled states and spacetime “atoms” (n = 1, 2, 3). A densely connected network serves as a crude, discrete representation of smooth spacetime at vast scales. A first-order phase transition from the free fermionic gas to the fermionic condensate created by the maximally entangled states of spacetime's atoms can be used to describe this phenomenon. Before the Grand Unification Epoch, this shift and the creation of our universe took place. He demonstrates how the network describes disconnected, discrete space at high temperatures. The system goes through a phase change at Planck's temperature, and at low temperatures, the space is converted to a triangulated discrete space. Due to vacuum fluctuations, spacetime's topology is very complicated. These variations result in the formation of the foamy structure that micro-universes connected by Einstein-Rosen bridges with wormhole topology may develop. The “foamy” structure, similar to Wheeler's “spacetime foam,” makes a major contribution to the effective cosmological constant, which is governed by the universe's Euler characteristic. The problem of “The Worst Theoretical Prediction in the History of Physics” may now be resolved thanks to his method. The suggested method, which does not have the fine-tuning issue brought on by the cosmological constant, can be viewed as a self-tuning solution to the cosmological problem.

I recommend publishing this article in its present form.

 

Author Response

We thank the referee for the valuable comments and suggestions.

Reviewer 4 Report

The paper looks at space-time complex networks and their possible connection to the cosmological constant. The paper is ok and can in principle be published, but I suggest the following changes:

1) Author should discuss the relation of his work to previous work presented by Bianconi et al in Scientific Reports 5:13979 (2015), which seems to contain similar ideas.

2) Last 4 lines of the manuscript should be deleted (lines 214-217). I think the statement is not true. All that is done in this paper is to look at a different microscopic, discrete space-time model, but it does not solve the cosmological constant problem at all. Hence the sentence in lines 214-17 is misleading and should be deleted.

 

Author Response

Point 1: Author should discuss the relation of his work to previous work presented by Bianconi et al in Scientific Reports 5:13979 (2015), which seems to contain similar ideas.

Response 1. The relation of our study to previous work by Bianconi et al., published in Scientific Reports, 5:13979 (2015), is explained in the  Introduction and the Discussions and Conclusion section of the revised manuscript.

Point 2: Last 4 lines of the manuscript should be deleted (lines 214-217). I think the statement is not true. All that is done in this paper is to look at a different microscopic, discrete space-time model, but it does not solve the cosmological constant problem at all. Hence the sentence in lines 214-17 is misleading and should be deleted.

Response 2. We disagree that the solution to the cosmological constant problem is not suggested in the present paper. Our findings show that a non-trivial topology of the universe is mandatory for a non-vanishing cosmological constant. The obtained dependence of the cosmological constant on the Euler characteristic (Eq.(40)) can be considered a self-tuning solution to the cosmological constant problem. The section "Discussions and conlusion" is rewritten to clarify this point.

We are thankful to the referee for the helpful remarks and suggestions.