Anthropic selection in a model with negative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:math> plus axion dark energy

We study a dark energy model composed of a bare negative cosmological constant and a single ultralight axion, motivated by the string axiverse. Assuming that intelligent observers arise and observe, as in our Universe, the onset of dark-energy-driven acceleration following matter domination, and that this acceleration persists to the present, we derive nontrivial constraints on both the axion mass and the bare cosmological constant. The axion mass is bounded from above to avoid fine-tuning of the initial misalignment angle near the hilltop, and from below because too light axions cannot achieve accelerated expansion due to their limited energy budget. As a result, the anthropically allowed axion mass range typically lies around <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>m</a:mi> <a:mo>=</a:mo> <a:mi mathvariant="script">O</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>10</a:mn> <a:mo stretchy="false">)</a:mo> <a:msub> <a:mi>H</a:mi> <a:mn>0</a:mn> </a:msub> </a:math> for a decay constant close to the Planck scale, where <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mi>H</f:mi> <f:mn>0</f:mn> </f:msub> </f:math> is the observed value of the Hubble constant. In this framework, the dark energy equation-of-state parameter <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>w</h:mi> <h:mn>0</h:mn> </h:msub> </h:math> generically deviates from <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mo>−</j:mo> <j:mn>1</j:mn> </j:math> by <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi mathvariant="script">O</l:mi> <l:mo stretchy="false">(</l:mo> <l:mn>0.1</l:mn> <l:mo stretchy="false">)</l:mo> </l:math> , providing a natural explanation for why <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>w</q:mi> <q:mo>≠</q:mo> <q:mo>−</q:mo> <q:mn>1</q:mn> </q:math> may be expected. We also find that, for a decay constant slightly smaller than the Planck scale, the peak value of dark energy density is significantly smaller than the anthropic bound on the cosmological constant and can be close to the observed value. These outcomes are intriguingly consistent with recent DESI hints of time-varying dark energy, and offer a compelling anthropic explanation within the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi mathvariant="normal">Λ</s:mi> <s:mo>+</s:mo> </s:math> axion framework.