Kaluza-Klein graviton freeze-in and big bang nucleosynthesis

In models featuring extra spatial dimensions, particle collisions in the early Universe can produce Kaluza-Klein gravitons. Such particles will later decay, potentially impacting the process of big bang nucleosynthesis. In this paper, we consider scenarios in which gravity is free to propagate throughout <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>n</a:mi></a:math> flat, compactified extra dimensions, while the fields of the Standard Model are confined to a (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>3</c:mn><c:mo>+</c:mo><c:mn>1</c:mn></c:mrow></c:math>)-dimensional brane. We calculate the production and decay rates of the states that make up the Kaluza-Klein graviton tower and determine the evolution of their abundances in the early Universe. We then go on to evaluate the impact of these decays on the resulting light element abundances. We identify significant regions of previously unexplored parameter space that are inconsistent with measurements of the primordial helium and deuterium abundances. In particular, we find that for the case of one extra dimension (two extra dimensions), the fundamental scale of gravity must be <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msub><e:mrow><e:mi>M</e:mi></e:mrow><e:mrow><e:mo>⋆</e:mo></e:mrow></e:msub><e:mo>≳</e:mo><e:mn>2</e:mn><e:mo>×</e:mo><e:msup><e:mrow><e:mn>10</e:mn></e:mrow><e:mrow><e:mn>13</e:mn></e:mrow></e:msup><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>GeV</e:mi></e:mrow></e:math> (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msub><g:mrow><g:mi>M</g:mi></g:mrow><g:mrow><g:mo>⋆</g:mo></g:mrow></g:msub><g:mo>≳</g:mo><g:mn>1</g:mn><g:msup><g:mrow><g:mn>0</g:mn></g:mrow><g:mrow><g:mn>10</g:mn></g:mrow></g:msup><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>GeV</g:mi></g:mrow></g:math>) unless the temperature of the early Universe was never greater than <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>T</i:mi><i:mo>∼</i:mo><i:mn>2</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi>TeV</i:mi></i:math> (<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>T</k:mi><k:mo>∼</k:mo><k:mn>1</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>GeV</k:mi></k:math>). For larger values of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>n</m:mi></m:math>, these constraints are less stringent. For the case of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>n</o:mi><o:mo>=</o:mo><o:mn>6</o:mn></o:math>, for example, our analysis excludes all values of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>M</q:mi><q:mo>⋆</q:mo></q:msub></q:math> less than <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mo>∼</s:mo><s:msup><s:mn>10</s:mn><s:mn>6</s:mn></s:msup><s:mtext> </s:mtext><s:mtext> </s:mtext><s:mi>GeV</s:mi></s:math>, unless the temperature of the Universe was never greater than <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>T</u:mi><u:mo>∼</u:mo><u:mn>3</u:mn><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mi>TeV</u:mi></u:math>. The results presented here severely limit the possibility that black holes were efficiently produced through particle collisions in the early Universe’s thermal bath. Published by the American Physical Society 2024