English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The homogeneous Friedman-Lema\^\i tre-Robertson-Walker (FLRW) cosmology of afree scalar field with vanishing cosmological constant was recently shown to beinvariant under the one-dimensional conformal group $\textrm{SL}(2,\mathbb{R})$acting as M{\"o}bius transformations on the proper time. Here we generalizethis analysis to arbitrary transformations of the proper time, $\tau\mapsto\tilde{\tau}=f(\tau)$, which are not to be confused with reparametrizations ofthe time coordinate. First, we show that the FLRW cosmology with anon-vanishing cosmological constant $\Lambda\ne 0$ is also invariant under a$\textrm{SL}(2,\mathbb{R})$ group of conformal transformations. The associatedconformal Noether charges form a $\mathfrak{sl}(2,\mathbb{R})$ Lie algebrawhich encodes the cosmic evolution. Second, we show that a cosmologicalconstant can be generated from the $\Lambda=0$ case through particularconformal transformations, realizing a compactification or de-compactificationof the proper time depending on the sign of $\Lambda$. Finally, we propose anextended FLRW cosmological action invariant under the full group$\textrm{Diff}({\cal S}^1)$ of conformal transformations on the proper time, bypromoting the cosmological constant to a gauge field for conformaltransformations or by modifying the scalar field action to a Schwarzian action.Such a conformally-invariant cosmology leads to a renewed problem of time andto the necessity to re-think inflation in purely time-deparameterized terms.

The Cosmological Constant from Conformal Transformations: M\"{o}bius Invariance and Schwarzian Action