Engaging with the digital world, there lies an influential community of wordsmiths who have adeptly married the art of writing with their profound experiences of motherhood: US Mommy Bloggers. This group is not bound by geographical location or socio-economic status, but rather a shared experience, the transition to motherhood, and their commitment to documenting this journey online. What started as a small niche in the early 2000s has now evolved into a significant cultural force, shaping parenting trends and consumer behavior across the nation and, indeed, the globe.

The term 'Mommy Blogger' is a colloquial yet widely accepted vernacular, used to describe a mother who maintains a blog - an online journal where she shares personal narratives, advice, and product reviews relating to parenthood. However, to limit the influence of these bloggers to the realm of parenting would be myopic. The themes they tackle range from education, health, and lifestyle to personal finance, self-care, and mental health. It is the vastness of these topics that allows them to reach diverse audiences, hence, amplifying their sphere of influence.

When analyzing the impact of these bloggers, the concept of 'diffusion of innovations theory' is particularly pertinent. As Everett Roger’s groundbreaking work suggests, innovations disseminate through social systems via communication channels. In this context, the 'innovation' could be a parenting trend or a product, and mommy bloggers represent an influential communication channel within the social system of parenity.

Their posts, shared widely across numerous digital platforms, are consumed by a vast audience, transforming these bloggers into opinion leaders within their respective communities. Furthermore, through their authentic, relatable narratives, they effectively bridge the gap between the innovators (product manufacturers, for instance) and the late majority or laggards in the adoption process. By doing so, they expedite the diffusion of trends across the social system, thereby shaping discourse and behavior relating to parenity.

Moreover, the influence these bloggers wield can be quantified using a mathematical construct called the 'h-index' borrowed from academic publishing. A blogger's h-index is a measure of the impact and reach of their posts based on the number of times they are cited (shared, commented on) by others. A high h-index indicates a blogger's significant influence within the digital community and beyond.

This influence, however, is not wielded without a delicate balance of responsibility and authenticity. The power to mold societal attitudes and trends comes with an inherent mandate to ensure the dissemination of accurate, responsible content. This ethical impasse is at the heart of the mommy blogging ecosystem, making it an intriguing field to explore from a sociological perspective.

Furthermore, the influence of mommy bloggers has been recognized and leveraged by marketers and public relations professionals. Their blogs are seen as fertile ground for product placement and influencer marketing, given their captive, engaged audience. This symbiotic relationship between bloggers and marketers is a fascinating study of how traditional advertising paradigms are evolving in the digital age.

The digital landscape is a breeding ground for cultural shifts, and the rise of mommy bloggers in the US is a testament to this fact. By leveraging their personal experiences and the power of the written word, they have carved a niche for themselves as credible influencers, shaping parenting trends and consumer behavior on a scale that was inconceivable before the digital revolution. The why, the how, and the what of their influence is a multidimensional equation, a confluence of sociology, technology, marketing, and the universal experience of parenthood. The fact that this equation is continually evolving makes the phenomenon of mommy bloggers an intellectually enriching and captivating field to explore.